-
2
-
-
85119562501
-
-
P. Alexandroff, H. Hopf, Topologie, Chelsea, New York, 1965 (original edition, Berlin, Germany, 1935).
-
-
-
-
3
-
-
85119562550
-
-
E.L. Allgower K. Georg Numerical Continuation Methods Series in Computers and Mathematics Vol. 13 1990 Springer New York
-
(1990)
-
-
Allgower, E.L.1
Georg, K.2
-
4
-
-
70350662980
-
Numerical path following
-
E.L. Allgower K. Georg Numerical path following P.G. Ciarlet J.L. Lions Handbook of Numerical Analysis, Vol. V 1997 North-Holland Amsterdam 3 207
-
(1997)
, pp. 3-207
-
-
Allgower, E.L.1
Georg, K.2
-
5
-
-
85119557315
-
-
E.L. Allgower, K. Georg, Piecewise linear methods for nonlinear equations and optimization, J. Comput. Appl. Math. 124 (2000) 245–261, this issue.
-
-
-
-
6
-
-
0022048415
-
An algorithm for piecewise linear approximation of an implicitly defined manifold
-
E.L. Allgower P.H. Schmidt An algorithm for piecewise linear approximation of an implicitly defined manifold SIAM J. Numer. Anal. 22 1985 322 346
-
(1985)
SIAM J. Numer. Anal.
, vol.22
, pp. 322-346
-
-
Allgower, E.L.1
Schmidt, P.H.2
-
7
-
-
0026240956
-
Simplicial pivoting for mesh generation of implicitly defined surfaces
-
E.L. Allgower S. Gnutzmann Simplicial pivoting for mesh generation of implicitly defined surfaces Comput. Aided Geom. Design 8 1991 305 325
-
(1991)
Comput. Aided Geom. Design
, vol.8
, pp. 305-325
-
-
Allgower, E.L.1
Gnutzmann, S.2
-
8
-
-
85119552748
-
-
R.E. Bank PLTMG: A Software Package for Solving Elliptic Partial Differential Equations Frontiers in Applied Mathematics Vol. 15 1994 SIAM Philadelphia, PA
-
(1994)
-
-
Bank, R.E.1
-
9
-
-
85119562557
-
-
F. Brezzi, J. Rappaz, P.A. Raviart, Finite dimensional approximation of nonlinear problems, Part I: Branches of nonsingular solutions, Numer. Math. 36 (1981) 1–25; Part II: Limit points, Numer. Math. 37 (1981) 1–28; Part III: Simple bifurcation points, Numer. Math. 38 (1981) 1–30.
-
-
-
-
10
-
-
85119551574
-
-
M.L. Brodzik, Numerical approximation of manifolds and applications, Ph.D. Thesis, Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 1996.
-
-
-
-
12
-
-
84966216764
-
Finding zeros of maps: Homotopy applications to continuation methods
-
S.N. Chow J. Mallett-Paret J.A. Yorke Finding zeros of maps: Homotopy applications to continuation methods Math. Comput. 32 1978 887 899
-
(1978)
Math. Comput.
, vol.32
, pp. 887-899
-
-
Chow, S.N.1
Mallett-Paret, J.2
Yorke, J.A.3
-
13
-
-
0025417986
-
On the computation of manifolds of foldpoints for parameter-dependent problems
-
R.X. Dai W.C. Rheinboldt On the computation of manifolds of foldpoints for parameter-dependent problems SIAM J. Numer. Anal. 27 1990 437 446
-
(1990)
SIAM J. Numer. Anal.
, vol.27
, pp. 437-446
-
-
Dai, R.X.1
Rheinboldt, W.C.2
-
14
-
-
0023401540
-
Efficient numerical path-following beyond critical points
-
P. Deuflhard B. Fiedler P. Kunkel Efficient numerical path-following beyond critical points SIAM J. Numer. Anal. 24 1987 912 927
-
(1987)
SIAM J. Numer. Anal.
, vol.24
, pp. 912-927
-
-
Deuflhard, P.1
Fiedler, B.2
Kunkel, P.3
-
15
-
-
0004599093
-
On the discretization error of parametrized nonlinear equations
-
J.P. Fink W.C. Rheinboldt On the discretization error of parametrized nonlinear equations SIAM J. Numer. Anal. 20 1983 732 746
-
(1983)
SIAM J. Numer. Anal.
, vol.20
, pp. 732-746
-
-
Fink, J.P.1
Rheinboldt, W.C.2
-
16
-
-
0023366430
-
A geometric framework for the numerical study of singular points
-
J.P. Fink W.C. Rheinboldt A geometric framework for the numerical study of singular points SIAM J. Numer. Anal. 24 1987 618 633
-
(1987)
SIAM J. Numer. Anal.
, vol.24
, pp. 618-633
-
-
Fink, J.P.1
Rheinboldt, W.C.2
-
17
-
-
85119559299
-
-
M. Golubitzky D.G. Schaeffer Singularities and Groups in Bifurcation Theory, Vol. I 1985 Springer New York
-
(1985)
-
-
Golubitzky, M.1
Schaeffer, D.G.2
-
19
-
-
85119557887
-
-
B. Hong, Computational methods for bifurcation problems with symmetries on the manifold, Ph.D. Thesis, University of Pittsburgh, Department of Mathematics, Pittsburgh, PA, 1991.
-
-
-
-
20
-
-
0003080367
-
Global homotopies and Newton methods
-
H.B. Keller Global homotopies and Newton methods C. de Boor G.H. Golub Recent Advances in Numerical Analysis 1978 Academic Press New York 73 94
-
(1978)
, pp. 73-94
-
-
Keller, H.B.1
-
21
-
-
85119563159
-
-
H.B. Keller Lectures on Numerical Methods in Bifurcation Problems 1987 Springer New York
-
(1987)
-
-
Keller, H.B.1
-
22
-
-
0000288810
-
Une méthode de résolution d'une catégorie d’équations transcendentes
-
E. Lahaye Une méthode de résolution d'une catégorie d’équations transcendentes C.R. Acad. Sci. Paris 198 1934 1840 1942
-
(1934)
C.R. Acad. Sci. Paris
, vol.198
, pp. 1840-1942
-
-
Lahaye, E.1
-
23
-
-
0020288760
-
A comparison of methods for determining turning points of nonlinear equations
-
R. Melhem W.C. Rheinboldt A comparison of methods for determining turning points of nonlinear equations Computing 29 1982 201 226
-
(1982)
Computing
, vol.29
, pp. 201-226
-
-
Melhem, R.1
Rheinboldt, W.C.2
-
24
-
-
0029346823
-
A new algorithm for two-dimensional continuation
-
R. Melville S. Mackey A new algorithm for two-dimensional continuation Comput. Math. Appl. 30 1995 31 46
-
(1995)
Comput. Math. Appl.
, vol.30
, pp. 31-46
-
-
Melville, R.1
Mackey, S.2
-
25
-
-
85119549444
-
-
A.P. Morgan Solving Polynomial Systems using Continuation for Engineering and Scientific Problems 1987 Prentice-Hall Englewood Cliffs, NJ
-
(1987)
-
-
Morgan, A.P.1
-
26
-
-
85119563132
-
-
J.M. Ortega W.C. Rheinboldt Iterative Solutions of Nonlinear Equations in Several Variables 1970 Academic Press New York
-
(1970)
-
-
Ortega, J.M.1
Rheinboldt, W.C.2
-
27
-
-
0342950709
-
On a computational method for the second fundamental tensor and its application to bifurcation problems
-
P.J. Rabier W.C. Rheinboldt On a computational method for the second fundamental tensor and its application to bifurcation problems Numer. Math. 57 1990 681 694
-
(1990)
Numer. Math.
, vol.57
, pp. 681-694
-
-
Rabier, P.J.1
Rheinboldt, W.C.2
-
28
-
-
0001509743
-
Solution fields of nonlinear equations and continuation methods
-
W.C. Rheinboldt Solution fields of nonlinear equations and continuation methods SIAM J. Numer. Anal. 17 1980 221 237
-
(1980)
SIAM J. Numer. Anal.
, vol.17
, pp. 221-237
-
-
Rheinboldt, W.C.1
-
29
-
-
0000256568
-
On the computation of multi-dimensional solution manifolds of parametrized equations
-
W.C. Rheinboldt On the computation of multi-dimensional solution manifolds of parametrized equations Numer. Math. 53 1988 165 181
-
(1988)
Numer. Math.
, vol.53
, pp. 165-181
-
-
Rheinboldt, W.C.1
-
30
-
-
0027574655
-
On the sensitivity of parametrized equations
-
W.C. Rheinboldt On the sensitivity of parametrized equations SIAM J. Numer. Anal. 30 1993 305 320
-
(1993)
SIAM J. Numer. Anal.
, vol.30
, pp. 305-320
-
-
Rheinboldt, W.C.1
-
31
-
-
0030378528
-
MANPACK: a set of algorithms for computations on implicitly defined manifolds
-
W.C. Rheinboldt MANPACK: a set of algorithms for computations on implicitly defined manifolds Comput. Math. Appl. 27 1996 15 28
-
(1996)
Comput. Math. Appl.
, vol.27
, pp. 15-28
-
-
Rheinboldt, W.C.1
-
32
-
-
85119565126
-
-
W.C. Rheinboldt Methods for Solving Systems of Nonlinear Equations 1998 SIAM Philadelphia, PA
-
(1998)
-
-
Rheinboldt, W.C.1
-
33
-
-
85119558000
-
-
J. Schwartz Nonlinear functional analysis (1963/64) 1964 Courant Institute of Mathematics and Science New York
-
(1964)
-
-
Schwartz, J.1
-
34
-
-
85119549576
-
-
R. Seydel, BIFPACK: a program package for continuation, bifurcation, and stability analysis, Technical Report Version 2.3+, University of Ulm, Germany, 1991.
-
-
-
-
35
-
-
0001861435
-
Some remarks on Bezout's theorem and complexity theory
-
M. Shub Some remarks on Bezout's theorem and complexity theory M.W. Hirsch J.E. Marsden M. Shub From Topology to Computation 1993 Springer Berlin 443 455
-
(1993)
, pp. 443-455
-
-
Shub, M.1
-
36
-
-
0028516294
-
Complexity of Bezout's theorem, Part V. Polynomial time
-
M. Shub S. Smale Complexity of Bezout's theorem, Part V. Polynomial time Theoret. Comput. Sci. 133 1994 141 164
-
(1994)
Theoret. Comput. Sci.
, vol.133
, pp. 141-164
-
-
Shub, M.1
Smale, S.2
-
37
-
-
85119559647
-
-
M.J. Todd, The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 124, Springer, New York, 1976.
-
-
-
-
38
-
-
85119559588
-
-
T. Tsuchiya, A priori and a posteriori error estimates of finite element solutions of parametrized nonlinear equations, Ph.D. Thesis, Department of Mathematics, University of Maryland, College Park, MD, 1990.
-
-
-
-
39
-
-
0023415939
-
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
-
L.T. Watson S.C. Billups A.P. Morgan Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms ACM Trans. Math. Software 13 1987 281 310
-
(1987)
ACM Trans. Math. Software
, vol.13
, pp. 281-310
-
-
Watson, L.T.1
Billups, S.C.2
Morgan, A.P.3
-
41
-
-
85119549950
-
-
S.M. Wise, A.J. Sommese, L.T. Watson, POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations, ACM Trans. Math. Software, to appear.
-
-
-
|