-
1
-
-
0007062667
-
Fast local convergence with single and multistep methods for nonlinear equations
-
J. P. Abbott and R. P. Brent (1975), 'Fast local convergence with single and multistep methods for nonlinear equations', Austr. Math. Soc. B 19, 173-199.
-
(1975)
Austr. Math. Soc. B
, vol.19
, pp. 173-199
-
-
Abbott, J.P.1
Brent, R.P.2
-
2
-
-
79957445719
-
-
ACRITH 1984, IBM High-Accuracy Arithmetic Subroutine Library ACRITH, Release 1, IBM Deutschland GmbH, Böblingen
-
ACRITH (1984), IBM High-Accuracy Arithmetic Subroutine Library (ACRITH), Release 1, IBM Deutschland GmbH, Böblingen.
-
-
-
-
3
-
-
0003796630
-
-
Academic Press, New York
-
R. A. Adams (1975), Sobolev Spaces, Academic Press, New York.
-
(1975)
Sobolev Spaces
-
-
Adams, R.A.1
-
4
-
-
79957477623
-
-
private communication
-
G. Alefeld, private communication.
-
-
-
Alefeld, G.1
-
5
-
-
0001985536
-
Inclusion methods for systems of nonlinear equations
-
J. Herzberger, ed., Studies in Computational Mathematics, Elsevier, Amsterdam
-
G. Alefeld (1994), Inclusion methods for systems of nonlinear equations. In Topics in Validated Computations (J. Herzberger, ed.), Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 7-26.
-
(1994)
Topics in Validated Computations
, pp. 7-26
-
-
Alefeld, G.1
-
7
-
-
0031487487
-
On the shape of the symmetric, persymmetric, and skew-symmetric solution set
-
G. Alefeld, V. Kreinovich and G. Mayer (1997), 'On the shape of the symmetric, persymmetric, and skew-symmetric solution set', SIAM J. Matrix Anal. Appl. 18, 693-705.
-
(1997)
SIAM J. Matrix Anal. Appl.
, vol.18
, pp. 693-705
-
-
Alefeld, G.1
Kreinovich, V.2
Mayer, G.3
-
8
-
-
0037336036
-
On the solution sets of particular classes of linear interval systems
-
DOI 10.1016/S0377-0427(02)00693-3, PII S0377042702006933
-
G. Alefeld, V. Kreinovich and G. Mayer (2003), 'On the solution sets of particular classes of linear interval systems', J. Comput. Appl. Math. 152, 1-15. (Pubitemid 36290360)
-
(2003)
Journal of Computational and Applied Mathematics
, vol.152
, Issue.1-2
, pp. 1-15
-
-
Alefeld, G.1
Kreinovich, V.2
Mayer, G.3
-
9
-
-
0003706460
-
-
2nd edn, SIAM, Philadelphia
-
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. C. Sorensen (1995), LAPACK User's Guide, Release 2.0, 2nd edn, SIAM, Philadelphia.
-
(1995)
LAPACK User's Guide, Release 2.0
-
-
Anderson, E.1
Bai, Z.2
Bischof, C.3
Demmel, J.4
Dongarra, J.5
Du Croz, J.6
Greenbaum, A.7
Hammarling, S.8
McKenney, A.9
Ostrouchov, S.10
Sorensen, D.C.11
-
10
-
-
11844296207
-
Affine arithmetic. Extended abstract
-
presented at, St. Petersburg
-
M. V. A. Andrade, J. L. D. Comba and J. Stolfi (1994), Affine arithmetic. Extended abstract, presented at INTERVAL'94, St. Petersburg.
-
(1994)
INTERVAL'94
-
-
Andrade, M.V.A.1
Comba, J.L.D.2
Stolfi, J.3
-
11
-
-
2442512882
-
-
ARITHMOS, Siemens AG, Bibl.-Nr. U 2900-I-Z87-1 edition
-
ARITHMOS (1986), ARITHMOS: Benutzerhandbuch, Siemens AG, Bibl.-Nr. U 2900-I-Z87-1 edition.
-
(1986)
ARITHMOS: Benutzerhandbuch
-
-
-
13
-
-
84937078021
-
Signed-digit number representations for fast parallel arithmetic
-
A. Avizienis (1961), 'Signed-digit number representations for fast parallel arithmetic', Ire Trans. Electron. Comp. EC-10, 389-400.
-
(1961)
Ire Trans. Electron. Comp.
, vol.EC-10
, pp. 389-400
-
-
Avizienis, A.1
-
17
-
-
85013507985
-
Inclusions for eigenvalues of selfadjoint problems
-
J. Herzberger, ed., Studies in Computational Mathematics, Elsevier, Amsterdam
-
H. Behnke and F. Goerisch (1994), Inclusions for eigenvalues of selfadjoint problems. In Topics in Validated Computations (J. Herzberger, ed.), Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 277-322.
-
(1994)
Topics in Validated Computations
, pp. 277-322
-
-
Behnke, H.1
Goerisch, F.2
-
18
-
-
0003878614
-
-
SIAM, Philadelphia
-
A. Ben-Tal and A. Nemirovskii (2001), Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia.
-
(2001)
Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
-
-
Ben-Tal, A.1
Nemirovskii, A.2
-
19
-
-
79957519153
-
-
Ariadna id: 04/4105, Contract Number: 18851/05/NL/MV
-
F. Bernelli Zazzera, M. Vasile, M. Massari and P. di Lizia (2004), Assessing the accuracy of interval arithmetic estimates in space flight mechanics. Final report, Ariadna id: 04/4105, Contract Number: 18851/05/NL/MV.
-
(2004)
Assessing the Accuracy of Interval Arithmetic Estimates in Space Flight Mechanics. Final Report
-
-
Bernelli Zazzera, F.1
Vasile, M.2
Massari, M.3
Di Lizia, P.4
-
21
-
-
0003019087
-
New methods for high-dimensional verified quadrature
-
M. Berz and K. Makino (1999), 'New methods for high-dimensional verified quadrature', Reliable Computing 5, 13-22. (Pubitemid 129579067)
-
(1999)
Reliable Computing
, vol.5
, Issue.1
, pp. 13-22
-
-
Berz, M.1
Makino, K.2
-
22
-
-
0004101619
-
-
Mathematics and Computer Science Division, Argonne National Laboratory
-
C. H. Bischof, A. Carle, G. Corliss and A. Griewank (1991), ADIFOR: Generating derivative codes from Fortran programs. Technical report, Mathematics and Computer Science Division, Argonne National Laboratory.
-
(1991)
ADIFOR: Generating Derivative Codes from Fortran Programs. Technical Report
-
-
Bischof, C.H.1
Carle, A.2
Corliss, G.3
Griewank, A.4
-
23
-
-
0033295839
-
SDPLIB 1.2: A library of semidefinite programming test problems
-
B. Borchers (1999), 'SDPLIB 1.2: A library of semidefinite programming test problems', Optim. Methods Software 11, 683-690.
-
(1999)
Optim. Methods Software
, vol.11
, pp. 683-690
-
-
Borchers, B.1
-
24
-
-
31544464919
-
-
SIAM, Philadelphia
-
F. Bornemann, D. Laurie, S. Wagon and J. Waldvogel (2004), The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia.
-
(2004)
The SIAM 100-Digit Challenge: A Study in High-accuracy Numerical Computing
-
-
Bornemann, F.1
Laurie, D.2
Wagon, S.3
Waldvogel, J.4
-
25
-
-
4243533815
-
-
Freiburger Intervall-Ber. 78/2, Institut für Angewandte Mathematik, Universität Freiburg
-
N. C. Börsken (1978), Komplexe Kreis-Standardfunktionen. Diplomarbeit, Freiburger Intervall-Ber. 78/2, Institut für Angewandte Mathematik, Universität Freiburg.
-
(1978)
Komplexe Kreis-standardfunktionen. Diplomarbeit
-
-
Börsken, N.C.1
-
27
-
-
33645900267
-
A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam
-
DOI 10.1016/j.jde.2005.07.016, PII S0022039605002639
-
B. Breuer, J. Horák, P. J. McKenna and M. Plum (2006), 'A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam', J. Diff. Equations 224, 60-97. (Pubitemid 43585102)
-
(2006)
Journal of Differential Equations
, vol.224
, Issue.1
, pp. 60-97
-
-
Breuer, B.1
Horak, J.2
McKenna, P.J.3
Plum, M.4
-
28
-
-
0344152908
-
Multiple solutions for a semilinear boundary value problem: A computational multiplicity proof
-
DOI 10.1016/S0022-0396(03)00186-4
-
B. Breuer, P. J. McKenna and M. Plum (2003), 'Multiple solutions for a semilinear boundary value problem: A computational multiplicity proof', J. Diff. Equations 195, 243-269. (Pubitemid 37457223)
-
(2003)
Journal of Differential Equations
, vol.195
, Issue.1
, pp. 243-269
-
-
Breuer, B.1
McKenna, P.J.2
Plum, M.3
-
29
-
-
0034509268
-
On a computer assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm-Liouville problem
-
DOI 10.1016/S0377-0427(00)00481-7
-
B. M. Brown, D. K. R. McCormack and A. Zettl (2000), 'On a computer assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm-Liouville problem', J. Comput. Appl. Math. 125, 385-393. (Pubitemid 32034887)
-
(2000)
Journal of Computational and Applied Mathematics
, vol.125
, Issue.1-2
, pp. 385-393
-
-
Brown, B.M.1
McCormack, D.K.R.2
Zettl, A.3
-
30
-
-
79957530793
-
Is a math proof a proof if no one can check it?
-
December 1988
-
M. W. Browne (1988), Is a math proof a proof if no one can check it? The New York Times, December 1988, p. 1.
-
(1988)
The New York Times
, pp. 1
-
-
Browne, M.W.1
-
31
-
-
0000118074
-
The strong stability of algorithms for solving symmetric linear systems
-
J. R. Bunch, J. W. Demmel and C. F. Van Loan (1989), 'The strong stability of algorithms for solving symmetric linear systems', SIAM J. Matrix Anal. Appl. 10, 494-499.
-
(1989)
SIAM J. Matrix Anal. Appl.
, vol.10
, pp. 494-499
-
-
Bunch, J.R.1
Demmel, J.W.2
Van Loan, C.F.3
-
32
-
-
79957513868
-
-
private communication
-
F. Bünger (2008), private communication.
-
(2008)
-
-
Bünger, F.1
-
33
-
-
0346362744
-
Iterative methods for interval inclusion of fixed points
-
O. Caprani and K. Madsen (1978), 'Iterative methods for interval inclusion of fixed points', BIT Numer. Math. 18, 42-51.
-
(1978)
BIT Numer. Math.
, vol.18
, pp. 42-51
-
-
Caprani, O.1
Madsen, K.2
-
35
-
-
0000474504
-
A mountain pass method for the numerical solutions of semilinear elliptic problems
-
Y. S. Choi and P. J. McKenna (1993), 'A mountain pass method for the numerical solutions of semilinear elliptic problems', Nonlinear Anal. Theory Methods Appl. 20, 417-437.
-
(1993)
Nonlinear Anal. Theory Methods Appl.
, vol.20
, pp. 417-437
-
-
Choi, Y.S.1
McKenna, P.J.2
-
36
-
-
0039606929
-
Einschließungssatz für die charakteristischen Zahlen von Matrizen
-
L. Collatz (1942), 'Einschließungssatz für die charakteristischen Zahlen von Matrizen', Math. Z. 48, 221-226.
-
(1942)
Math. Z
, vol.48
, pp. 221-226
-
-
Collatz, L.1
-
37
-
-
0005546339
-
Adaptive, self-validating numerical quadrature
-
G. F. Corliss and L. B. Rall (1987), 'Adaptive, self-validating numerical quadrature', SIAM J. Sci. Statist. Comput. 8, 831-847.
-
(1987)
SIAM J. Sci. Statist. Comput.
, vol.8
, pp. 831-847
-
-
Corliss, G.F.1
Rall, L.B.2
-
38
-
-
0003495675
-
-
Springer
-
G. Corliss, C. Faure, A. Griewank, L. Hascöet and U. Nauman (2002), Automatic Differentiation of Algorithms: From Simulation to Optimization, Springer.
-
(2002)
Automatic Differentiation of Algorithms: From Simulation to Optimization
-
-
Corliss, G.1
Faure, C.2
Griewank, A.3
Hascöet, L.4
Nauman, U.5
-
39
-
-
0034952666
-
A remarkable example of catastrophic cancellation unraveled
-
DOI 10.1007/s006070170028
-
A. Cuyt, B. Verdonk, S. Becuwe and P. Kuterna (2001), 'A remarkable example of catastrophic cancellation unraveled', Computing 66, 309-320. (Pubitemid 32609030)
-
(2001)
Computing (Vienna/New York)
, vol.66
, Issue.3
, pp. 309-320
-
-
Cuyt, A.1
Verdonk, B.2
Becuwe, S.3
Kuterna, P.4
-
40
-
-
13844254046
-
On the superlinear Lazer-McKenna conjecture
-
DOI 10.1016/j.jde.2004.07.017, PII S0022039604003183
-
E. N. Dancer and S. S. Yan (2005), 'On the superlinear Lazer-McKenna conjecture', J. Diff. Equations 210, 317-351. (Pubitemid 40251067)
-
(2005)
Journal of Differential Equations
, vol.210
, Issue.2
, pp. 317-351
-
-
Dancer, E.N.1
Yan, S.2
-
41
-
-
29244445741
-
Sur les développements en série des fonctions d'une seule variable
-
G. Darboux (1876), 'Sur les développements en série des fonctions d'une seule variable', J. des Mathématiques Pures et Appl. 3, 291-312.
-
(1876)
J. Des. Mathématiques Pures et Appl.
, vol.3
, pp. 291-312
-
-
Darboux, G.1
-
43
-
-
0000810983
-
A floating-point technique for extending the available precision
-
T. J. Dekker (1971), 'A floating-point technique for extending the available precision', Numer. Math. 18, 224-242.
-
(1971)
Numer. Math.
, vol.18
, pp. 224-242
-
-
Dekker, T.J.1
-
44
-
-
0003886379
-
-
Department of Computer Science, University of Tennessee, Knoxville, TN, USA
-
J. B. Demmel (1989), On floating point errors in Cholesky. LAPACK Working Note 14 CS-89-87, Department of Computer Science, University of Tennessee, Knoxville, TN, USA.
-
(1989)
On Floating Point Errors in Cholesky. LAPACK Working Note 14 CS-89-87
-
-
Demmel, J.B.1
-
45
-
-
0000847923
-
On the complexity of computing error bounds
-
DOI 10.1007/s10208001004
-
J. B. Demmel, B. Diament and G. Malajovich (2001), 'On the complexity of computing error bounds', Found. Comput. Math. 1, 101-125. (Pubitemid 33681691)
-
(2001)
Foundations of Computational Mathematics
, vol.1
, Issue.1
, pp. 101-125
-
-
Demmel, J.1
Diament, B.2
Malajovich, G.3
-
46
-
-
58149398431
-
Accurate and efficient expression evaluation and linear algebra
-
Cambridge University Press
-
J. B. Demmel, I. Dumitriu, O. Holtz and P. Koev (2008), Accurate and efficient expression evaluation and linear algebra. In Acta Numerica, Vol. 17, Cambridge University Press, pp. 87-145.
-
(2008)
Acta Numerica
, vol.17
, pp. 87-145
-
-
Demmel, J.B.1
Dumitriu, I.2
Holtz, O.3
Koev, P.4
-
47
-
-
79957534351
-
-
University of California, Berkeley
-
J. B. Demmel, Y. Hida, W. Kahan, X. S. Li, S. Mukherjee and E. J. Riedy (2004), Error bounds from extra precise iterative refinement. Report no. ucb/csd-04-1344, Computer Science Devision (EECS), University of California, Berkeley.
-
(2004)
Error Bounds from Extra Precise Iterative Refinement. Report No. Ucb/csd-04-1344, Computer Science Devision (EECS)
-
-
Demmel, J.B.1
Hida, Y.2
Kahan, W.3
Li, X.S.4
Mukherjee, S.5
Riedy, E.J.6
-
49
-
-
0000802374
-
The approximation of one matrix by another of lower rank
-
C. Eckart and G. Young (1936), 'The approximation of one matrix by another of lower rank', Psychometrika 1, 211-218.
-
(1936)
Psychometrika
, vol.1
, pp. 211-218
-
-
Eckart, C.1
Young, G.2
-
50
-
-
0011534940
-
A computer-assisted proof of universality for area-preserving maps
-
J.-P. Eckmann, H. Koch and P. Wittwer (1984), 'A computer-assisted proof of universality for area-preserving maps', Mem. Amer. Math. Soc. 47, 289.
-
(1984)
Mem. Amer. Math. Soc.
, vol.47
, pp. 289
-
-
Eckmann, J.-P.1
Koch, H.2
Wittwer, P.3
-
53
-
-
10044296444
-
Affine arithmetic: Concepts and applications
-
DOI 10.1023/B:NUMA.0000049462.70970.b6
-
L. H. de Figueiredo and J. Stolfi (2004), 'Affine arithmetic: Concepts and applications', Numer. Algorithms 37, 147-158. (Pubitemid 39604462)
-
(2004)
Numerical Algorithms
, vol.37
, Issue.1-4 SPEC. ISS.
, pp. 147-158
-
-
De Figueiredo, L.H.1
Stolfi, J.2
-
54
-
-
21844502046
-
Gaussian elimination with partial pivoting can fail in practice
-
L. V. Foster (1994), 'Gaussian elimination with partial pivoting can fail in practice', SIAM J. Matrix Anal. Appl. 14, 1354-1362.
-
(1994)
SIAM J. Matrix Anal. Appl.
, vol.14
, pp. 1354-1362
-
-
Foster, L.V.1
-
55
-
-
33746886718
-
-
INRIA. Code and documentation available at
-
L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier and P. Zimmermann (2005), MPFR: A multiple-precision binary floating-point library with correct rounding. Research Report RR-5753, INRIA. Code and documentation available at: http://hal.inria.fr/inria-00000818.
-
(2005)
MPFR: A Multiple-precision Binary Floating-point Library with Correct Rounding. Research Report RR-5753
-
-
Fousse, L.1
Hanrot, G.2
Lefèvre, V.3
Pélissier, P.4
Zimmermann, P.5
-
56
-
-
79957523869
-
Proving conjectures by use of interval arithmetic
-
U. Kulisch et al., ed., Springer
-
A. Frommer (2001), Proving conjectures by use of interval arithmetic. In Perspectives on Enclosure Methods: SCAN 2000 (U. Kulisch et al., ed.), Springer.
-
(2001)
Perspectives on Enclosure Methods: SCAN 2000
-
-
Frommer, A.1
-
57
-
-
0001201892
-
Computer assisted proof of chaos in the Lorenz equations
-
PII S0167278997002339
-
Z. Galias and P. Zgliczynski (1998), 'Computer assisted proof of chaos in the Lorenz equations', Physica D 115, 165-188. (Pubitemid 128676553)
-
(1998)
Physica D: Nonlinear Phenomena
, vol.115
, Issue.3-4
, pp. 165-188
-
-
Galias, Z.1
Zgliczynski, P.2
-
58
-
-
34250456039
-
Circular arithmetic and the determination of polynomial zeros
-
I. Gargantini and P. Henrici (1972), 'Circular arithmetic and the determination of polynomial zeros', Numer. Math. 18, 305-320.
-
(1972)
Numer. Math.
, vol.18
, pp. 305-320
-
-
Gargantini, I.1
Henrici, P.2
-
59
-
-
34250271532
-
Symmetry and related problems via the maximum principle
-
B. Gidas, W. Ni and L. Nirenberg (1979), 'Symmetry and related problems via the maximum principle', Comm. Math. Phys. 68, 209-243.
-
(1979)
Comm. Math. Phys.
, vol.68
, pp. 209-243
-
-
Gidas, B.1
Ni, W.2
Nirenberg, L.3
-
61
-
-
0026122066
-
What every computer scientist should know about floating-point arithmetic
-
DOI 10.1145/103162.103163
-
D. Goldberg (1991), 'What every computer scientist should know about floatingpoint arithmetic', ACM Comput. Surv. 23, 5-48. (Pubitemid 21723680)
-
(1991)
ACM Computing Surveys
, vol.23
, Issue.1
, pp. 5-48
-
-
Goldberg David1
-
62
-
-
1942545052
-
From LCF to HOL: A short history
-
G. Plotkin, C. Stirling and M. Tofte, eds, MIT Press
-
M. J. C. Gordon (2000), From LCF to HOL: A short history. In Proof, Language, and Interaction: Essays in Honour of Robin Milner (G. Plotkin, C. Stirling and M. Tofte, eds), MIT Press. http://www.cl.cam.ac.uk/~mjcg/papers/ HolHistory.html.
-
(2000)
Proof, Language, and Interaction: Essays in Honour of Robin Milner
-
-
Gordon, M.J.C.1
-
63
-
-
84975511018
-
-
AMS, Providence, RI
-
D. Gorenstein, R. Lyons and R. Solomon (1994), The Classification of the Finite Simple Groups, Vol. 40 of Math. Surveys Monographs, AMS, Providence, RI.
-
(1994)
The Classification of the Finite Simple Groups, Vol. 40 of Math. Surveys Monographs
-
-
Gorenstein, D.1
Lyons, R.2
Solomon, R.3
-
64
-
-
24644437042
-
A mathematical view of automatic differentiation
-
Cambridge University Press
-
A. Griewank (2003), A mathematical view of automatic differentiation. In Acta Numerica, Vol. 12, Cambridge University Press, pp. 321-398.
-
(2003)
Acta Numerica
, vol.12
, pp. 321-398
-
-
Griewank, A.1
-
66
-
-
0006768428
-
The centered form
-
E. Hansen, ed., Oxford University Press
-
E. Hansen (1969), The centered form. In Topics in Interval Analysis (E. Hansen, ed.), Oxford University Press, pp. 102-106.
-
(1969)
Topics in Interval Analysis
, pp. 102-106
-
-
Hansen, E.1
-
67
-
-
0002662801
-
Interval arithmetic in matrix computations II
-
E. R. Hansen and R. Smith (1967), 'Interval arithmetic in matrix computations II', SIAM J. Numer. Anal. 4, 1-9.
-
(1967)
SIAM J. Numer. Anal.
, vol.4
, pp. 1-9
-
-
Hansen, E.R.1
Smith, R.2
-
68
-
-
3042546902
-
-
Master's thesis, University of Manchester
-
G. Hargreaves (2002), Interval analysis in MATLAB. Master's thesis, University of Manchester. http://www.manchester.ac.uk/mims/eprints.
-
(2002)
Interval Analysis in MATLAB
-
-
Hargreaves, G.1
-
70
-
-
38249010614
-
Componentwise perturbation theory for linear systems with multiple right-hand sides
-
D. J. Higham and N. J. Higham (1992a), 'Componentwise perturbation theory for linear systems with multiple right-hand sides', Linear Algebra Appl. 174, 111-129.
-
(1992)
Linear Algebra Appl.
, vol.174
, pp. 111-129
-
-
Higham, D.J.1
Higham, N.J.2
-
71
-
-
0000829895
-
Backward error and condition of structured linear systems
-
D. J. Higham and N. J. Higham (1992b), 'Backward error and condition of structured linear systems', SIAM J. Matrix Anal. Appl. 13, 162-175.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 162-175
-
-
Higham, D.J.1
Higham, N.J.2
-
75
-
-
0025725943
-
Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side
-
C. Jansson (1991), 'Interval linear systems with symmetric matrices, skew-symmetric matrices, and dependencies in the right hand side', Computing 46, 265-274. (Pubitemid 21707925)
-
(1991)
Computing (Vienna/New York)
, vol.46
, Issue.3
, pp. 265-274
-
-
Jansson, C.1
-
76
-
-
85013547269
-
On self-validating methods for optimization problems
-
J. Herzberger, ed., Studies in Computational Mathematics, Elsevier, Amsterdam
-
C. Jansson (1994), On self-validating methods for optimization problems. In Topics in Validated Computations (J. Herzberger, ed.), Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 381-438.
-
(1994)
Topics in Validated Computations
, pp. 381-438
-
-
Jansson, C.1
-
77
-
-
0031541012
-
Calculation of exact bounds for the solution set of linear interval systems
-
C. Jansson (1997), 'Calculation of exact bounds for the solution set of linear interval systems', Linear Algebra Appl. 251, 321-340.
-
(1997)
Linear Algebra Appl.
, vol.251
, pp. 321-340
-
-
Jansson, C.1
-
78
-
-
0942277397
-
A rigorous lower bound for the optimal value of convex optimization problems
-
C. Jansson (2004a), 'A rigorous lower bound for the optimal value of convex optimization problems', J. Global Optim. 28, 121-137.
-
(2004)
J. Global Optim.
, vol.28
, pp. 121-137
-
-
Jansson, C.1
-
79
-
-
2942630897
-
Rigorous lower and upper bounds in linear programming
-
DOI 10.1137/S1052623402416839
-
C. Jansson (2004b), 'Rigorous lower and upper bounds in linear programming', SIAM J. Optim. 14, 914-935. (Pubitemid 39073318)
-
(2004)
SIAM Journal on Optimization
, vol.14
, Issue.3
, pp. 914-935
-
-
Jansson, C.1
-
80
-
-
68949161452
-
VSDP: A MATLAB software package for verified semidefinite programming
-
C. Jansson (2006), VSDP: A MATLAB software package for verified semidefinite programming. In NOLTA 2006, pp. 327-330.
-
(2006)
NOLTA 2006
, pp. 327-330
-
-
Jansson, C.1
-
81
-
-
77149142275
-
On verified numerical computations in convex programming
-
C. Jansson (2009), 'On verified numerical computations in convex programming', Japan J. Indust. Appl. Math. 26, 337-363.
-
(2009)
Japan J. Indust. Appl. Math.
, vol.26
, pp. 337-363
-
-
Jansson, C.1
-
82
-
-
0033239809
-
An algorithm for checking regularity of interval matrices
-
PII S0895479896313978
-
C. Jansson and J. Rohn (1999), 'An algorithm for checking regularity of interval matrices', SIAM J. Matrix Anal. Appl. 20, 756-776. (Pubitemid 129332600)
-
(1999)
SIAM Journal on Matrix Analysis and Applications
, vol.20
, Issue.3
, pp. 756-776
-
-
Jansson, C.1
Rohn, J.2
-
83
-
-
55549133270
-
Rigorous error bounds for the optimal value in semidefinite programming
-
C. Jansson, D. Chaykin and C. Keil (2007), 'Rigorous error bounds for the optimal value in semidefinite programming', SIAM J. Numer. Anal. 46, 180-200. http://link.aip.org/link/?SNA/46/180/1.
-
(2007)
SIAM J. Numer. Anal.
, vol.46
, pp. 180-200
-
-
Jansson, C.1
Chaykin, D.2
Keil, C.3
-
84
-
-
0003608168
-
-
Lecture notes for a summer course at the University of Michigan
-
W. M. Kahan (1968), A more complete interval arithmetic. Lecture notes for a summer course at the University of Michigan.
-
(1968)
A More Complete Interval Arithmetic
-
-
Kahan, W.M.1
-
85
-
-
0032684913
-
Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence
-
Y. Kanzawa and S. Oishi (1999a), 'Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence', IEICE Trans. Fundamentals E82-A, 1062-1069.
-
(1999)
IEICE Trans. Fundamentals
, vol.E82-A
, pp. 1062-1069
-
-
Kanzawa, Y.1
Oishi, S.2
-
86
-
-
0032668746
-
Calculating bifurcation points with guaranteed accuracy
-
Y. Kanzawa and S. Oishi (1999b), 'Calculating bifurcation points with guaranteed accuracy', IEICE Trans. Fundamentals E82-A, 1055-1061.
-
(1999)
IEICE Trans. Fundamentals
, vol.E82-A
, pp. 1055-1061
-
-
Kanzawa, Y.1
Oishi, S.2
-
88
-
-
0031082710
-
Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems
-
PII S1064827594266131
-
R. B. Kearfott (1997), 'Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems', SIAM J. Sci. Comput. 18, 574-594. (Pubitemid 127642986)
-
(1997)
SIAM Journal of Scientific Computing
, vol.18
, Issue.2
, pp. 574-594
-
-
Kearfott, R.B.1
-
89
-
-
0041395623
-
INTLIB: A portable Fortran-77 elementary function library
-
R. B. Kearfott, M. Dawande, K. du and C. Hu (1992), 'INTLIB: A portable Fortran-77 elementary function library', Interval Comput. 3, 96-105.
-
(1992)
Interval Comput.
, vol.3
, pp. 96-105
-
-
Kearfott, R.B.1
Dawande, M.2
Du, K.3
Hu, C.4
-
90
-
-
0034446065
-
Existence verification for singular zeros complex nonlinear systems
-
PII S0036142999361074
-
R. B. Kearfott, J. Dian and A. Neumaier (2000), 'Existence verification for singular zeros of complex nonlinear systems', SIAM J. Numer. Anal. 38, 360-379. (Pubitemid 33779237)
-
(2000)
SIAM Journal on Numerical Analysis
, vol.38
, Issue.2
, pp. 360-379
-
-
Kearfott, R.B.1
Dian, J.2
Neumaier, A.3
-
91
-
-
77954708057
-
Standardized notation in interval analysis
-
Melentiev Energy Systems Institute SB RAS, Irkutsk
-
R. B. Kearfott, M. T. Nakao, A. Neumaier, S. M. Rump, S. P. Shary and P. van Hentenfyck (2005) Standardized notation in interval analysis. In Proc. XIII Baikal International School-Seminar: Optimization Methods and their Applications, Vol. 4, Melentiev Energy Systems Institute SB RAS, Irkutsk.
-
(2005)
Proc. XIII Baikal International School-seminar: Optimization Methods and Their Applications
, vol.4
-
-
Kearfott, R.B.1
Nakao, M.T.2
Neumaier, A.3
Rump, S.M.4
Shary, S.P.5
Van Hentenfyck, P.6
-
92
-
-
68949160521
-
Lurupa: Rigorous error bounds in linear programming
-
B. Buchberger, S. Oishi, M. Plum and S. M. Rump, eds, Vol. 05391 of Dagstuhl Seminar Proceedings, Internationales Begegnungs-und Forschungszentrum für Informatik IBFI, Schloss Dagstuhl, Germany
-
C. Keil (2006), Lurupa: Rigorous error bounds in linear programming. In Algebraic and Numerical Algorithms and Computer-assisted Proofs (B. Buchberger, S. Oishi, M. Plum and S. M. Rump, eds), Vol. 05391 of Dagstuhl Seminar Proceedings, Internationales Begegnungs-und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany. http://drops.dagstuhl.de/opus/ volltexte/2006/445.
-
(2006)
Algebraic and Numerical Algorithms and Computer-assisted Proofs
-
-
Keil, C.1
-
93
-
-
33746930599
-
Computational experience with rigorous error bounds for the netlib linear programming library
-
DOI 10.1007/s11155-006-9004-7
-
C. Keil and C. Jansson (2006), 'Computational experience with rigorous error bounds for the Netlib linear programming library', Reliable Computing 12, 303-321. http://www.optimization-online.org/DB HTML/2004/12/1018.html. (Pubitemid 44199972)
-
(2006)
Reliable Computing
, vol.12
, Issue.4
, pp. 303-321
-
-
Keil, C.1
Jansson, C.2
-
94
-
-
0004084795
-
-
Springer, Berlin
-
R. Klatte, U. Kulisch, A. Wiethoff, C. Lawo and M. Rauch (1993), C-XSC A C++ Class Library for Extended Scientific Computing, Springer, Berlin.
-
(1993)
C-XSC A C++ Class Library for Extended Scientific Computing
-
-
Klatte, R.1
Kulisch, U.2
Wiethoff, A.3
Lawo, C.4
Rauch, M.5
-
95
-
-
0001292188
-
PROFIL/BIAS: A fast interval library
-
O. Knüppel (1994), 'PROFIL/BIAS: A fast interval library', Computing 53, 277-287.
-
(1994)
Computing
, vol.53
, pp. 277-287
-
-
Knüppel, O.1
-
98
-
-
0030825213
-
Use of interval slopes in implementing an interval method for global nonlinear DC circuit analysis
-
L. V. Kolev and V. Mladenov (1997), Use of interval slopes in implementing an interval method for global nonlinear DC circuit analysis. Internat. J. Circuit Theory Appl. 12, 37-42.
-
(1997)
Internat. J. Circuit Theory Appl.
, vol.12
, pp. 37-42
-
-
Kolev, L.V.1
Mladenov, V.2
-
101
-
-
0000446186
-
Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
-
R. Krawczyk (1969a), 'Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken', Computing 4, 187-201.
-
(1969)
Computing
, vol.4
, pp. 187-201
-
-
Krawczyk, R.1
-
102
-
-
0043059444
-
Fehlerabschätzung reeller Eigenwerte und Eigenvektoren von Matrizen
-
R. Krawczyk (1969b), 'Fehlerabschätzung reeller Eigenwerte und Eigenvektoren von Matrizen', Computing 4, 281-293.
-
(1969)
Computing
, vol.4
, pp. 281-293
-
-
Krawczyk, R.1
-
103
-
-
0022077080
-
Interval slopes for rational functions and associated centered forms
-
R. Krawczyk and A. Neumaier (1985), 'Interval slopes for rational functions and associated centered forms', SIAM J. Numer. Anal. 22, 604-616. (Pubitemid 15511156)
-
(1985)
SIAM Journal on Numerical Analysis
, vol.22
, Issue.3
, pp. 604-616
-
-
Krawczyk, R.1
Neumaier, A.2
-
104
-
-
0002561242
-
Optimal solution of interval linear systems is intractable (NP-hard)
-
V. Kreinovich, A. V. Lakeyev and S. I. Noskov (1993), 'Optimal solution of interval linear systems is intractable (NP-hard) ', Interval Comput. 1, 6-14.
-
(1993)
Interval Comput.
, vol.1
, pp. 6-14
-
-
Kreinovich, V.1
Lakeyev, A.V.2
Noskov, S.I.3
-
107
-
-
0012031633
-
Etude statistique des erreurs dans l'arithmétique des ordinateurs: Application au contrôle des résultats d'algorithmes númeriques
-
M. la Porte and J. Vignes (1974), 'Etude statistique des erreurs dans l'arithmétique des ordinateurs: Application au contrôle des résultats d'algorithmes númeriques', Numer. Math. 23, 63-72.
-
(1974)
Numer. Math.
, vol.23
, pp. 63-72
-
-
La Porte, M.1
Vignes, J.2
-
109
-
-
1542406165
-
A computer-assisted instability proof for the Orr-sommerfeld equation with Blasius profile
-
J. Lahmann and M. Plum (2004), 'A computer-assisted instability proof for the Orr-Sommerfeld equation with Blasius profile', Z. Angew. Math. Mech. 84, 188-204.
-
(2004)
Z. Angew. Math. Mech.
, vol.84
, pp. 188-204
-
-
Lahmann, J.1
Plum, M.2
-
110
-
-
0000853821
-
The nonexistence of finite projective planes of order 10
-
C. W. H. Lam, L. Thiel and S. Swiercz (1989), 'The nonexistence of finite projective planes of order 10', Canad. J. Math. 41, 1117-1123.
-
(1989)
Canad. J. Math.
, vol.41
, pp. 1117-1123
-
-
Lam, C.W.H.1
Thiel, L.2
Swiercz, S.3
-
111
-
-
0039742356
-
Optimale Eigenwerteinschließung
-
N. J. Lehmann (1963), 'Optimale Eigenwerteinschließung', Numer. Math. 5, 246-272.
-
(1963)
Numer. Math.
, vol.5
, pp. 246-272
-
-
Lehmann, N.J.1
-
112
-
-
19044370033
-
Design, implementation and testing of extended and mixed precision BLAS
-
DOI 10.1145/567806.567808
-
X. S. Li, J. W. Demmel, D. H. Bailey, G. Henry, Y. Hida, J. Iskandar, W. Kahan, S. Y. Kang, A. Kapur, M. C. Martin, B. J. Thompson, T. Tung and D. J. Yoo (2002), 'Design, implementation and testing of extended and mixed precision BLAS', ACM Trans. Math. Software 28, 152-205. (Pubitemid 135701674)
-
(2002)
ACM Transactions on Mathematical Software
, vol.28
, Issue.2
, pp. 152-205
-
-
Li, X.1
Demmel, J.W.2
Bailey, D.H.3
Henry, G.4
Hida, Y.5
Iskandar, J.6
Kahan, W.7
Kang, S.Y.8
Kapur, A.9
Martin, M.C.10
Thompson, B.J.11
Tung, T.12
Yoo, D.J.13
-
113
-
-
0036605359
-
Rump's example revisited
-
DOI 10.1023/A:1015569431383
-
E. Loh and W. Walster (2002), 'Rump's example revisited', Reliable Computing 8, 245-248. (Pubitemid 34562698)
-
(2002)
Reliable Computing
, vol.8
, Issue.3
, pp. 245-248
-
-
Loh, E.1
William Walster, G.2
-
115
-
-
79957463140
-
-
Maple 2009, Release 13, Reference Manual
-
Maple (2009), Release 13, Reference Manual.
-
-
-
-
116
-
-
0013364106
-
The contribution of T. Sunaga to interval analysis and reliable computing
-
T. Csendes, ed., Kluwer
-
S. Markov and K. Okumura (1999), The contribution of T. Sunaga to interval analysis and reliable computing. In Developments in Reliable Computing (T. Csendes, ed.), Kluwer, pp. 167-188.
-
(1999)
Developments in Reliable Computing
, pp. 167-188
-
-
Markov, S.1
Okumura, K.2
-
118
-
-
0003699119
-
-
MATLAB, The MathWorks
-
MATLAB (2004), User's Guide, Version 7, The MathWorks.
-
(2004)
User's Guide, Version 7
-
-
-
120
-
-
0004293209
-
-
Prentice-Hall, Englewood Cliffs
-
R. E. Moore (1966), Interval Analysis, Prentice-Hall, Englewood Cliffs.
-
(1966)
Interval Analysis
-
-
Moore, R.E.1
-
121
-
-
0000805856
-
A test for existence of solutions for non-linear systems
-
R. E. Moore (1977), 'A test for existence of solutions for non-linear systems', SIAM J. Numer. Anal. 4, 611-615.
-
(1977)
SIAM J. Numer. Anal.
, vol.4
, pp. 611-615
-
-
Moore, R.E.1
-
122
-
-
34547686767
-
The dawning
-
R. E. Moore (1999), 'The dawning', Reliable Computing 5, 423-424.
-
(1999)
Reliable Computing
, vol.5
, pp. 423-424
-
-
Moore, R.E.1
-
124
-
-
77955911632
-
-
Birkhäuser, Boston
-
J.-M. Muller, N. Brisebarre, F. de Dinechin, C.-P. Jeannerod, V. Lefèvre, G. Melquiond, R. Revol, D. Stehlé and S. Torres (2009), Handbook of Floating-Point Arithmetic, Birkhäuser, Boston.
-
(2009)
Handbook of Floating-point Arithmetic
-
-
Muller, J.-M.1
Brisebarre, N.2
De Dinechin, F.3
Jeannerod, C.-P.4
Lefèvre, V.5
Melquiond, G.6
Revol, R.7
Stehlé, D.8
Torres, S.9
-
125
-
-
0033154252
-
An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness
-
K. Nagatou, M. T. Nakao and N. Yamamoto (1999), 'An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness', Numer. Funct. Anal. Optim. 20, 543-565.
-
(1999)
Numer. Funct. Anal. Optim.
, vol.20
, pp. 543-565
-
-
Nagatou, K.1
Nakao, M.T.2
Yamamoto, N.3
-
126
-
-
0002301249
-
A numerical approach to the proof of existence of solutions for elliptic problems
-
M. T. Nakao (1988), 'A numerical approach to the proof of existence of solutions for elliptic problems', Japan J. Appl. Math. 5, 313-332.
-
(1988)
Japan J. Appl. Math.
, vol.5
, pp. 313-332
-
-
Nakao, M.T.1
-
127
-
-
0001452218
-
-1type residual iteration
-
-1type residual iteration. Computing (Suppl.) 9, 161-173.
-
(1993)
Computing (Suppl.)
, vol.9
, pp. 161-173
-
-
Nakao, M.T.1
-
128
-
-
0000566179
-
Numerical verifications for solutions to elliptic equations using residual iterations with higher order finite elements
-
M. T. Nakao and N. Yamamoto (1995), 'Numerical verifications for solutions to elliptic equations using residual iterations with higher order finite elements', J. Comput. Appl. Math. 60, 271-279.
-
(1995)
J. Comput. Appl. Math.
, vol.60
, pp. 271-279
-
-
Nakao, M.T.1
Yamamoto, N.2
-
129
-
-
23744514537
-
A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
-
DOI 10.1007/s00607-004-0111-1
-
M. T. Nakao, K. Hashimoto and Y. Watanabe (2005), 'A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems', Computing 75, 1-14. (Pubitemid 41118332)
-
(2005)
Computing (Vienna/New York)
, vol.75
, Issue.1 SPEC. ISS.
, pp. 1-14
-
-
Nakao, M.T.1
Hashimoto, K.2
Watanabe, Y.3
-
131
-
-
18744367980
-
ODE software that computes guaranteed bounds on the solution
-
H. P. Langtangen, A. M. Bruaset and E. Quak, eds, Springer
-
N. S. Nedialkov and K. R. Jackson (2000), ODE software that computes guaranteed bounds on the solution. In Advances in Software Tools for Scientic Computing (H. P. Langtangen, A. M. Bruaset and E. Quak, eds), Springer, pp. 197-224.
-
(2000)
Advances in Software Tools for Scientic Computing
, pp. 197-224
-
-
Nedialkov, N.S.1
Jackson, K.R.2
-
133
-
-
0015982207
-
Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen
-
A. Neumaier (1974), 'Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen', Z. Angew. Math. Mech. 54, 39-51.
-
(1974)
Z. Angew. Math. Mech.
, vol.54
, pp. 39-51
-
-
Neumaier, A.1
-
134
-
-
0000546454
-
New techniques for the analysis of linear interval equations
-
A. Neumaier (1984), 'New techniques for the analysis of linear interval equations', Linear Algebra Appl. 58, 273-325.
-
(1984)
Linear Algebra Appl.
, vol.58
, pp. 273-325
-
-
Neumaier, A.1
-
135
-
-
0023288173
-
Overestimation in linear interval equations
-
A. Neumaier (1987), 'Overestimation in linear interval equations', SIAM J. Numer. Anal. 24, 207-214.
-
(1987)
SIAM J. Numer. Anal.
, vol.24
, pp. 207-214
-
-
Neumaier, A.1
-
136
-
-
0024135848
-
An existence test for root clusters and multiple roots
-
A. Neumaier (1988), 'An existence test for root clusters and multiple roots', Z. Angew. Math. Mech. 68, 256-257.
-
(1988)
Z. Angew. Math. Mech.
, vol.68
, pp. 256-257
-
-
Neumaier, A.1
-
137
-
-
0001861349
-
Rigorous sensitivity analysis for parameter-dependent systems of equations
-
A. Neumaier (1989), 'Rigorous sensitivity analysis for parameter-dependent systems of equations', J. Math. Anal. Appl. 144, 16-25.
-
(1989)
J. Math. Anal. Appl.
, vol.144
, pp. 16-25
-
-
Neumaier, A.1
-
138
-
-
0003915794
-
-
Encyclopedia of Mathematics and its Applications, Cambridge University Press
-
A. Neumaier (1990), Interval Methods for Systems of Equations, Encyclopedia of Mathematics and its Applications, Cambridge University Press.
-
(1990)
Interval Methods for Systems of Equations
-
-
Neumaier, A.1
-
139
-
-
0012226884
-
The wrapping effect, ellipsoid arithmetic, stability and confidence regions
-
A. Neumaier (1993), 'The wrapping effect, ellipsoid arithmetic, stability and confidence regions', Computing Supplementum 9, 175-190.
-
(1993)
Computing Supplementum
, vol.9
, pp. 175-190
-
-
Neumaier, A.1
-
141
-
-
0036680537
-
Grand challenges and scientific standards in interval analysis
-
DOI 10.1023/A:1016341317043
-
A. Neumaier (2002), 'Grand challenges and scientific standards in interval analysis', Reliable Computing 8, 313-320. (Pubitemid 34798603)
-
(2002)
Reliable Computing
, vol.8
, Issue.4
, pp. 313-320
-
-
Neumaier, A.1
-
142
-
-
0042342393
-
Enclosing clusters of zeros of polynomials
-
DOI 10.1016/S0377-0427(03)00380-7
-
A. Neumaier (2003), 'Enclosing clusters of zeros of polynomials', J. Comput. Appl. Math. 156, 389-401. (Pubitemid 36910933)
-
(2003)
Journal of Computational and Applied Mathematics
, vol.156
, Issue.2
, pp. 389-401
-
-
Neumaier, A.1
-
143
-
-
2942655185
-
Complete search in continuous global optimization and constraint satisfaction
-
A. Neumaier (2004), Complete search in continuous global optimization and constraint satisfaction. In Acta Numerica, Vol. 13, Cambridge University Press, pp. 271-369. (Pubitemid 38773595)
-
(2004)
Acta Numerica
, vol.13
, pp. 271-369
-
-
Neumaier, A.1
-
145
-
-
84872739236
-
Improving interval enclosures
-
To appear
-
A. Neumaier (2010), 'Improving interval enclosures', Reliable Computing. To appear.
-
(2010)
Reliable Computing
-
-
Neumaier, A.1
-
146
-
-
0001029040
-
Rigorous chaos verification in discrete dynamical systems
-
A. Neumaier and T. Rage (1993), 'Rigorous chaos verification in discrete dynamical systems', Physica D 67, 327-346.
-
(1993)
Physica D
, vol.67
, pp. 327-346
-
-
Neumaier, A.1
Rage, T.2
-
147
-
-
2942641986
-
Safe bounds in linear and mixed-integer linear programming
-
DOI 10.1007/s10107-003-0433-3
-
A. Neumaier and O. Shcherbina (2004), 'Safe bounds in linear and mixed-integer programming', Math. Program. A 99, 283-296. (Pubitemid 40871723)
-
(2004)
Mathematical Programming
, vol.99
, Issue.2
, pp. 283-296
-
-
Neumaier, A.1
Shcherbina, O.2
-
148
-
-
33845220799
-
Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
-
W. Oettli and W. Prager (1964.), 'Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides', Numer. Math. 6, 405-409
-
(1964)
Numer. Math.
, vol.6
, pp. 405-409
-
-
Oettli, W.1
Prager, W.2
-
149
-
-
0038449954
-
Fast verification of solutions for sparse monotone matrix equations
-
T. Ogita, S. Oishi and Y. Ushiro (2001), 'Fast verification of solutions for sparse monotone matrix equations', Comput. Suppl. 15, 175-187.
-
(2001)
Comput. Suppl.
, vol.15
, pp. 175-187
-
-
Ogita, T.1
Oishi, S.2
Ushiro, Y.3
-
150
-
-
79957509109
-
-
S. Oishi 1998, private communication
-
S. Oishi (1998), private communication.
-
-
-
-
152
-
-
0036003238
-
Fast verification of solutions of matrix equations
-
DOI 10.1007/s002110100310
-
S. Oishi and S. M. Rump (2002), 'Fast verification of solutions of matrix equations', Numer. Math. 90, 755-773. (Pubitemid 36161560)
-
(2002)
Numerische Mathematik
, vol.90
, Issue.4
, pp. 755-773
-
-
Oishi, S.1
Rump, S.M.2
-
154
-
-
0036533553
-
Interval computation of Viswanath's constant
-
DOI 10.1023/A:1014702122205
-
J. B. Oliveira and L. H. de Figueiredo (2002) 'Interval computation of Viswanath's constant', Reliable Computing 8, 131-138. (Pubitemid 34254808)
-
(2002)
Reliable Computing
, vol.8
, Issue.2
, pp. 131-138
-
-
Oliveira, J.B.1
De Figueiredo, L.H.2
-
155
-
-
2442587863
-
Computational experience and the explanatory value of condition measures for linear optimization
-
DOI 10.1137/S1052623402401804
-
F. Ordóñez and R. M. Freund (2003), 'Computational experience and the explanatory value of condition measures for linear optimization', SIAM J. Optim. 14, 307-333. (Pubitemid 38614139)
-
(2004)
SIAM Journal on Optimization
, vol.14
, Issue.2
, pp. 307-333
-
-
Ordonez, F.1
Freund, R.M.2
-
158
-
-
0002765091
-
Radian reduction for trigonometric functions
-
M. Payne and R. Hanek (1983), 'Radian reduction for trigonometric functions', SIGNUM Newsletter 18, 19-24.
-
(1983)
SIGNUM Newsletter
, vol.18
, pp. 19-24
-
-
Payne, M.1
Hanek, R.2
-
159
-
-
0037102619
-
Self-validating integration and approximation of piecewise analytic functions
-
K. Petras (2002), 'Self-validating integration and approximation of piecewise analytic functions', J. Comput. Appl. Math. 145, 345-359.
-
(2002)
J. Comput. Appl. Math.
, vol.145
, pp. 345-359
-
-
Petras, K.1
-
160
-
-
0001810506
-
Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems
-
M. Plum (1992), 'Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems', Computing 49, 25-44.
-
(1992)
Computing
, vol.49
, pp. 25-44
-
-
Plum, M.1
-
161
-
-
0009869367
-
Enclosures for solutions of parameter-dependent nonlinear elliptic boundary value problems: Theory and implementation on a parallel computer
-
M. Plum (1994), 'Enclosures for solutions of parameter-dependent nonlinear elliptic boundary value problems: Theory and implementation on a parallel computer', Interval Comput. 3, 106-121.
-
(1994)
Interval Comput.
, vol.3
, pp. 106-121
-
-
Plum, M.1
-
162
-
-
0001486782
-
Existence and enclosure results for continua of solutions of parameter-dependent nonlinear boundary value problems
-
M. Plum (1995), 'Existence and enclosure results for continua of solutions of parameter-dependent nonlinear boundary value problems', J. Comput. Appl. Math. 60, 187-200.
-
(1995)
J. Comput. Appl. Math.
, vol.60
, pp. 187-200
-
-
Plum, M.1
-
163
-
-
0000298436
-
Enclosures for two-point boundary value problems near bifurcation points
-
Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, computer Arithmetic and Validated Numerics SCAN-95 held in Wuppertal, Germany, September 26-29, 1995
-
M. Plum (1996), Enclosures for two-point boundary value problems near bifurcation points. In Scientific Computing and Validated Numerics: Proc. International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, SCAN-95 (G. Alefeld et al., eds), Vol. 90 of Math. Res., Akademie Verlag, Berlin, pp. 265-279. (Pubitemid 126063881)
-
(1996)
Mathematical Research
, vol.90
, pp. 265-279
-
-
Plum, M.1
-
164
-
-
0000065403
-
Guaranteed numerical bounds for eigenvalues
-
Knoxville, TN, USA D. Hinton et al., eds, of Lect. Notes Pure Appl. Math., Marcel Dekker, New York
-
M. Plum (1997), 'Guaranteed numerical bounds for eigenvalues', In Spectral Theory and Computational Methods of Sturm-Liouville Problems: Proc. 1996 Conference, Knoxville, TN, USA (D. Hinton et al., eds), Vol. 191 of Lect. Notes Pure Appl. Math., Marcel Dekker, New York, pp. 313-332.
-
(1997)
Spectral Theory and Computational Methods of Sturm-liouville Problems: Proc. 1996 Conference
, vol.191
, pp. 313-332
-
-
Plum, M.1
-
165
-
-
68349108316
-
Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
-
M. Plum (2008), 'Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance', DMV Jahresbericht 110, 19-54.
-
(2008)
DMV Jahresbericht
, vol.110
, pp. 19-54
-
-
Plum, M.1
-
166
-
-
0037095611
-
New solutions of the Gelfand problem
-
M. Plum and C. Wieners (2002), 'New solutions of the Gelfand problem', J. Math. Anal. Appl. 269, 588-606.
-
(2002)
J. Math. Anal. Appl.
, vol.269
, pp. 588-606
-
-
Plum, M.1
Wieners, C.2
-
167
-
-
0027307460
-
Checking robust nonsingularity is NP-hard
-
S. Poljak and J. Rohn (1993), 'Checking robust nonsingularity is NP-hard', Math. Control, Signals, and Systems 6, 1-9. (Pubitemid 23690965)
-
(1993)
Mathematics of Control, Signals, and Systems
, vol.6
, Issue.1
, pp. 1-9
-
-
Poljak Svatopluk1
Rohn Jiri2
-
170
-
-
47849100672
-
ValEncIA-IVP: A comparison with other initial value problem solvers
-
SCAN, Duisburg
-
A. Rauh, E. Auer and E. P. Hofer (2006), ValEncIA-IVP: A comparison with other initial value problem solvers. In Proc. 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN, Duisburg.
-
(2006)
Proc. 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
-
-
Rauh, A.1
Auer, E.2
Hofer, E.P.3
-
171
-
-
0003395351
-
Variational methods in mathematics
-
2nd edn, Reidel, Dordrecht
-
K. Rektorys (1980), Variational methods in mathematics. In Science and Engineering, 2nd edn, Reidel, Dordrecht.
-
(1980)
Science and Engineering
-
-
Rektorys, K.1
-
173
-
-
84951900479
-
The problem of integration in finite terms
-
R. H. Risch (1969), 'The problem of integration in finite terms', Trans. Amer. Math. Soc. 139, 167-189.
-
(1969)
Trans. Amer. Math. Soc.
, vol.139
, pp. 167-189
-
-
Risch, R.H.1
-
174
-
-
0008671924
-
NP-hardness results for linear algebraic problems with interval data
-
J. Herzberger, ed., Studies in Computational Mathematics, Elsevier, Amsterdam
-
J. Rohn (1994), NP-hardness results for linear algebraic problems with interval data. In Topics in Validated Computations (J. Herzberger, ed.), Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 463-471.
-
(1994)
Topics in Validated Computations
, pp. 463-471
-
-
Rohn, J.1
-
176
-
-
70349464603
-
Forty necessary and sufficient conditions for regularity of interval matrices: A survey
-
J. Rohn (2009a), 'Forty necessary and sufficient conditions for regularity of interval matrices: A survey', Electron. J. Linear Algebra 18, 500-512.
-
(2009)
Electron. J. Linear Algebra
, vol.18
, pp. 500-512
-
-
Rohn, J.1
-
178
-
-
21844503702
-
Computing exact componentwise bounds on solutions of linear system is NP-hard
-
J. Rohn and V. Kreinovich (1995), 'Computing exact componentwise bounds on solutions of linear system is NP-hard', SIAM J. Matrix Anal. Appl. 16, 415-420.
-
(1995)
SIAM J. Matrix Anal. Appl.
, vol.16
, pp. 415-420
-
-
Rohn, J.1
Kreinovich, V.2
-
180
-
-
0003119522
-
Solving algebraic problems with high accuracy
-
Published in A New Approach to Scientific Computation U. W. Kulisch and W. L. Miranker, eds, Academic Press
-
S. M. Rump (1983), Solving algebraic problems with high accuracy. Habilitationsschrift, published in A New Approach to Scientific Computation (U. W. Kulisch and W. L. Miranker, eds), Academic Press, pp. 51-120.
-
(1983)
Habilitationsschrift
, pp. 51-120
-
-
Rump, S.M.1
-
181
-
-
78149317502
-
Rigorous sensitivity analysis for systems of linear and nonlinear equations
-
S. M. Rump (1990), 'Rigorous sensitivity analysis for systems of linear and nonlinear equations', Math. Comput. 54, 721-736.
-
(1990)
Math. Comput.
, vol.54
, pp. 721-736
-
-
Rump, S.M.1
-
182
-
-
33746928018
-
Verification methods for dense and sparse systems of equations
-
J. Herzberger, ed., Elsevier, Studies in Computational Mathematics, Amsterdam
-
S. M. Rump (1994), Verification methods for dense and sparse systems of equations. In Topics in Validated Computations (J. Herzberger, ed.), Elsevier, Studies in Computational Mathematics, Amsterdam, pp. 63-136.
-
(1994)
Topics in Validated Computations
, pp. 63-136
-
-
Rump, S.M.1
-
183
-
-
0002342184
-
INTLAB: INTerval LABoratory
-
T. Csendes, ed., Kluwer, Dordrecht
-
S. M. Rump (1999a), INTLAB: INTerval LABoratory. In Developments in Reliable Computing (T. Csendes, ed.), Kluwer, Dordrecht, pp. 77-104. http://www.ti3.tu-harburg.de/rump/intlab/index.html.
-
(1999)
Developments in Reliable Computing
, pp. 77-104
-
-
Rump, S.M.1
-
184
-
-
0042043158
-
Fast and parallel interval arithmetic
-
S. M. Rump (1999b), 'Fast and parallel interval arithmetic', BIT Numer. Math. 39, 539-560.
-
(1999)
BIT Numer. Math.
, vol.39
, pp. 539-560
-
-
Rump, S.M.1
-
185
-
-
0041694320
-
Rigorous and portable standard functions
-
S. M. Rump (2001a), Rigorous and portable standard functions. BIT Numer. Math. 41, 540-562. (Pubitemid 33636117)
-
(2001)
BIT Numerical Mathematics
, vol.41
, Issue.3
, pp. 540-562
-
-
Rump, S.M.1
-
186
-
-
0035587757
-
Computational error bounds for multiple or nearly multiple eigenvalues
-
S. M. Rump (2001b), 'Computational error bounds for multiple or nearly multiple eigenvalues', Linear Algebra Appl. 324, 209-226.
-
(2001)
Linear Algebra Appl.
, vol.324
, pp. 209-226
-
-
Rump, S.M.1
-
187
-
-
0041841198
-
Ten methods to bound multiple roots of polynomials
-
DOI 10.1016/S0377-0427(03)00381-9
-
S. M. Rump (2003a), 'Ten methods to bound multiple roots of polynomials', J. Comput. Appl. Math. 156, 403-432. (Pubitemid 36910934)
-
(2003)
Journal of Computational and Applied Mathematics
, vol.156
, Issue.2
, pp. 403-432
-
-
Rump, S.M.1
-
188
-
-
1342310025
-
Structured perturbations I: Normwise distances
-
S. M. Rump (2003b), 'Structured perturbations I: Normwise distances', SIAM J. Matrix Anal. Appl. 25, 1-30.
-
(2003)
SIAM J. Matrix Anal. Appl.
, vol.25
, pp. 1-30
-
-
Rump, S.M.1
-
189
-
-
1342288856
-
Structured perturbations II: Componentwise distances
-
S. M. Rump (2003c), 'Structured perturbations II: Componentwise distances', SIAM J. Matrix Anal. Appl. 25, 31-56.
-
(2003)
SIAM J. Matrix Anal. Appl.
, vol.25
, pp. 31-56
-
-
Rump, S.M.1
-
190
-
-
31544478845
-
Eigenvalues, pseudospectrum and structured perturbations
-
DOI 10.1016/j.laa.2005.06.009, PII S0024379505003034
-
S. M. Rump (2006), 'Eigenvalues, pseudospectrum and structured perturbations', Linear Algebra Appl. 413, 567-593. (Pubitemid 43153796)
-
(2006)
Linear Algebra and Its Applications
, vol.413
, Issue.2-3 SPEC. ISS.
, pp. 567-593
-
-
Rump, S.M.1
-
191
-
-
77956237657
-
Ultimately fast accurate summation
-
S. M. Rump (2009), 'Ultimately fast accurate summation', SIAM J. Sci. Comput. 31, 3466-3502.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 3466-3502
-
-
Rump, S.M.1
-
192
-
-
77953478326
-
Verified error bounds for multiple roots of systems of nonlinear equations
-
To appear in, published online at Numer Algor DOI 10.1007/s11075-009- 9339-3
-
S. M. Rump and S. Graillat (2009), Verified error bounds for multiple roots of systems of nonlinear equations. To appear in Numer. Algorithms; published online at Numer Algor DOI 10.1007/s11075-009-9339-3.
-
(2009)
Numer. Algorithms
-
-
Rump, S.M.1
Graillat, S.2
-
194
-
-
79957445206
-
The ratio between the Toeplitz and the unstructured condition number
-
S. M. Rump and H. Sekigawa (2009), 'The ratio between the Toeplitz and the unstructured condition number', Operator Theory: Advances and Applications 199, 397-419.
-
(2009)
Operator Theory: Advances and Applications
, vol.199
, pp. 397-419
-
-
Rump, S.M.1
Sekigawa, H.2
-
195
-
-
4043079134
-
On eigenvector bounds
-
DOI 10.1023/B:BITN.0000009941.51707.26
-
S. M. Rump and J. Zemke (2004), 'On eigenvector bounds', BIT Numer. Math. 43, 823-837. (Pubitemid 39064037)
-
(2003)
BIT Numerical Mathematics
, vol.43
, Issue.4
, pp. 823-837
-
-
Rump, S.M.1
Zemke, J.-P.M.2
-
196
-
-
55049129860
-
Accurate floating-point summation I: Faithful rounding
-
S. M. Rump, T. Ogita and S. Oishi (2008), 'Accurate floating-point summation I: Faithful rounding', SIAM J. Sci. Comput. 31, 189-224.
-
(2008)
SIAM J. Sci. Comput.
, vol.31
, pp. 189-224
-
-
Rump, S.M.1
Ogita, T.2
Oishi, S.3
-
197
-
-
21144437792
-
A polyhedral branch-and-cut approach to global optimization
-
DOI 10.1007/s10107-005-0581-8
-
N. V. Sahinidis and M. Tawaralani (2005), 'A polyhedral branch-and-cut approach to global optimization', Math. Program. B 103, 225-249. (Pubitemid 40878749)
-
(2005)
Mathematical Programming
, vol.103
, Issue.2
, pp. 225-249
-
-
Tawarmalani, M.1
Sahinidis, N.V.2
-
198
-
-
20144370424
-
Exclusion regions for systems of equations
-
DOI 10.1137/S0036142902418898
-
H. Schichl and A. Neumaier (2004), 'Exclusion regions for systems of equations', SIAM J. Numer. Anal. 42, 383-408. (Pubitemid 40408028)
-
(2004)
SIAM Journal on Numerical Analysis
, vol.42
, Issue.1
, pp. 383-408
-
-
Schichl, H.1
Neumaier, A.2
-
199
-
-
28044471201
-
Interval analysis on directed acyclic graphs for global optimization
-
DOI 10.1007/s10898-005-0937-x
-
H. Schichl and A. Neumaier (2005), 'Interval analysis on directed acyclic graphs for global optimization', J. Global Optim. 33, 541-562. (Pubitemid 41690335)
-
(2005)
Journal of Global Optimization
, vol.33
, Issue.4
, pp. 541-562
-
-
Schichl, H.1
Neumaier, A.2
-
200
-
-
0036792971
-
A new technique in systems analysis under interval uncertainty and ambiguity
-
S. P. Shary (2002), 'A new technique in systems analysis under interval uncertainty and ambiguity', Reliable Computing 8, 321-419.
-
(2002)
Reliable Computing
, vol.8
, pp. 321-419
-
-
Shary, S.P.1
-
201
-
-
0025566497
-
Stochastic perturbation theory
-
G. W. Stewart (1990), 'Stochastic perturbation theory', SIAM Rev. 32, 579-610.
-
(1990)
SIAM Rev.
, vol.32
, pp. 579-610
-
-
Stewart, G.W.1
-
202
-
-
79957478646
-
-
Master's thesis, University of Tokyo
-
T. Sunaga (1956), Geometry of numerals. Master's thesis, University of Tokyo.
-
(1956)
Geometry of Numerals
-
-
Sunaga, T.1
-
203
-
-
0002038715
-
Theory of an interval algebra and its application to numerical analysis
-
T. Sunaga (1958), 'Theory of an interval algebra and its application to numerical analysis', RAAG Memoirs 2, 29-46.
-
(1958)
RAAG Memoirs
, vol.2
, pp. 29-46
-
-
Sunaga, T.1
-
205
-
-
84903838644
-
Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM
-
Shiga, Japan
-
A. Takayasu, S. Oishi and T. Kubo (2009b), Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM. In Proc. Asia Simulation Conference 2009 (JSST 2009), Shiga, Japan, pp. 1-8.
-
(2009)
Proc. Asia Simulation Conference 2009 (JSST 2009)
, pp. 1-8
-
-
Takayasu, A.1
Oishi, S.2
Kubo, T.3
-
206
-
-
2942665751
-
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
-
DOI 10.1007/s10107-003-0467-6
-
M. Tawaralani and N. V. Sahinidis (2004), 'Global optimization of mixed-integer nonlinear programs: A theoretical and computational study', Math. Program. 99, 563-591. (Pubitemid 40871718)
-
(2004)
Mathematical Programming
, vol.99
, Issue.3
, pp. 563-591
-
-
Tawarmalani, M.1
Sahinidis, N.V.2
-
207
-
-
0000920501
-
Semidefinite programming
-
Cambridge University Press
-
M. J. Todd (2001), Semidefinite programming. In Acta Numerica, Vol. 10, Cambridge University Press, pp. 515-560.
-
(2001)
Acta Numerica
, vol.10
, pp. 515-560
-
-
Todd, M.J.1
-
208
-
-
6944242932
-
The SIAM 100-dollar, 100-digit challenge
-
L. N. Trefethen (2002), 'The SIAM 100-dollar, 100-digit challenge', SIAM-NEWS 35, 2. http://www.siam.org/siamnews/06-02/challengedigits.pdf.
-
(2002)
SIAM-NEWS
, vol.35
, pp. 2
-
-
Trefethen, L.N.1
-
210
-
-
0033563546
-
The Lorenz attractor exists
-
W. Tucker (1999), 'The Lorenz attractor exists', CR Acad. Sci., Paris, Sér. I, Math. 328, 1197-1202.
-
(1999)
CR Acad. Sci., Paris, Sér. I, Math.
, vol.328
, pp. 1197-1202
-
-
Tucker, W.1
-
211
-
-
3142743708
-
Solving semidefinite-quadratic-linear programs using SDPT3
-
DOI 10.1007/s10107-002-0347-5
-
R. H. Tütüncü, K. C. Toh and M. J. Todd (2003), 'Solving semidefinite-quadraticlinear programs using SDPT3', Math. Program. B 95, 189-217. (Pubitemid 44757853)
-
(2003)
Mathematical Programming, Series B
, vol.95
, Issue.2
, pp. 189-217
-
-
Tutuncu, R.H.1
Toh, K.C.2
Todd, M.J.3
-
212
-
-
0030106462
-
Semidefinite programming
-
L. Vandenberghe and S. Boyd (1996), 'Semidefinite programming', SIAM Review 38, 49-95. (Pubitemid 126610912)
-
(1996)
SIAM Review
, vol.38
, Issue.1
, pp. 49-95
-
-
Vandenberghe, L.1
Boyd, S.2
-
213
-
-
0018046614
-
New methods for evaluating the validity of the results of mathematical computations
-
DOI 10.1016/0378-4754(78)90016-2
-
J. Vignes (1978), 'New methods for evaluating the validity of the results of mathematical computations', Math. Comp. Simul. XX, 227-249. (Pubitemid 9419141)
-
(1978)
Mathematics and Computers in Simulation
, vol.20
, Issue.4
, pp. 227-249
-
-
Vignes, J.1
-
215
-
-
0034402963
-
Random Fibonacci sequences and the number 1.13198824
-
D. Viswanath (1999) 'Random Fibonacci sequences and the number 1.13198824...', Math. Comp. 69, 1131-1155.
-
(1999)
Math. Comp.
, vol.69
, pp. 1131-1155
-
-
Viswanath, D.1
-
218
-
-
0021418315
-
The computation of symmetry-breaking bifurcation points
-
B. Werner and A. Spence (1984), 'The computation of symmetry-breaking bifurcation points', SIAM J. Numer. Anal. 21, 388-399.
-
(1984)
SIAM J. Numer. Anal.
, vol.21
, pp. 388-399
-
-
Werner, B.1
Spence, A.2
-
220
-
-
0012033691
-
A collection of problems for which Gaussian elimination with partial pivoting is unstable
-
S. J. Wright (1993), 'A collection of problems for which Gaussian elimination with partial pivoting is unstable', SIAM J. Sci. Comput. 14, 231-238.
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 231-238
-
-
Wright, S.J.1
-
221
-
-
79957509591
-
A fast verified automatic integration algorithm using double exponential formula
-
N. Yamanaka, T. Okayama, S. Oishi and T. Ogita (2009), 'A fast verified automatic integration algorithm using double exponential formula', RIMS Kokyuroku 1638, 146-158.
-
(2009)
RIMS Kokyuroku
, vol.1638
, pp. 146-158
-
-
Yamanaka, N.1
Okayama, T.2
Oishi, S.3
Ogita, T.4
-
222
-
-
0001927944
-
The algebra of many-valued quantities
-
R. C. Young (1931), 'The algebra of many-valued quantities', Mathematische Annalen 104, 260-290.
-
(1931)
Mathematische Annalen
, vol.104
, pp. 260-290
-
-
Young, R.C.1
-
225
-
-
0005100397
-
Variational bounds to eigenvalues of selfadjoint eigenvalue problems with arbitrary spectrum
-
S. Zimmermann and U. Mertins (1995), 'Variational bounds to eigenvalues of selfadjoint eigenvalue problems with arbitrary spectrum', Z. Anal. Anwendungen 14, 327-345.
-
(1995)
Z. Anal. Anwendungen
, vol.14
, pp. 327-345
-
-
Zimmermann, S.1
Mertins, U.2
|