-
2
-
-
0001351705
-
On the augmented system approach to sparse least-squares problems
-
M. Arioli, I. S. Duff, and P. P. M. de Rijk, On the augmented system approach to sparse least-squares problems, Numer. Math. 55:667-684 (1989).
-
(1989)
Numer. Math.
, vol.55
, pp. 667-684
-
-
Arioli, M.1
Duff, I.S.2
De Rijk, P.P.M.3
-
3
-
-
0041658066
-
Accurate symmetric indefinite linear equation solvers
-
Manuscript, May
-
C. Ashcraft, R. G. Grimes, and J. G. Lewis, Accurate symmetric indefinite linear equation solvers, Manuscript, May 1995, to appear in SIAM J. Matrix Anal. Appl.
-
(1995)
SIAM J. Matrix Anal. Appl.
-
-
Ashcraft, C.1
Grimes, R.G.2
Lewis, J.G.3
-
4
-
-
0025445384
-
Computing accurate eigensystems of scaled diagonally dominant matrices
-
J. Barlow and J. Demmel, Computing accurate eigensystems of scaled diagonally dominant matrices, SIAM J. Numer. Anal. 27:762-791 (1990).
-
(1990)
SIAM J. Numer. Anal.
, vol.27
, pp. 762-791
-
-
Barlow, J.1
Demmel, J.2
-
5
-
-
0015200926
-
Analysis of the diagonal pivoting method
-
J. R. Bunch, Analysis of the diagonal pivoting method, SIAM J. Numer. Anal. 8:656-680 (1971).
-
(1971)
SIAM J. Numer. Anal.
, vol.8
, pp. 656-680
-
-
Bunch, J.R.1
-
6
-
-
84966228742
-
Some stable methods for calculating inertia and solving symmetric linear systems
-
J. R. Bunch and L. Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Math. Comp. 31:163-179 (1977).
-
(1977)
Math. Comp.
, vol.31
, pp. 163-179
-
-
Bunch, J.R.1
Kaufman, L.2
-
8
-
-
0015200767
-
Direct methods for solving symmetric indefinite systems of linear equations
-
J. R. Bunch and B. N. Parlett, Direct methods for solving symmetric indefinite systems of linear equations, SIAM J. Numer. Anal. 8:639-655 (1971).
-
(1971)
SIAM J. Numer. Anal.
, vol.8
, pp. 639-655
-
-
Bunch, J.R.1
Parlett, B.N.2
-
9
-
-
38249038136
-
Solving the algebraic Riccati equation with the matrix sign function
-
R. Byers, Solving the algebraic Riccati equation with the matrix sign function, Linear Algebra Appl. 85:267-279 (1987).
-
(1987)
Linear Algebra Appl.
, vol.85
, pp. 267-279
-
-
Byers, R.1
-
10
-
-
0002170151
-
Rank revealing QR factorizations
-
T. F. Chan, Rank revealing QR factorizations, Linear Algebra Appl. 88/89:67-82 (1987).
-
(1987)
Linear Algebra Appl.
, vol.88-89
, pp. 67-82
-
-
Chan, T.F.1
-
11
-
-
0003886379
-
On floating point errors in Cholesky
-
Computer Science Dept. Report, Univ. of Tennessee, Knoxville, Oct.
-
J. Demmel, On Floating Point errors in Cholesky, LAPACK Working Note 14, Computer Science Dept. Report, Univ. of Tennessee, Knoxville, Oct. 1989.
-
(1989)
LAPACK Working Note
, vol.14
-
-
Demmel, J.1
-
12
-
-
0041658067
-
-
personal communication
-
J. Demmel, personal communication, 1996.
-
(1996)
-
-
Demmel, J.1
-
13
-
-
21144468781
-
Jacobi's method is more accurate than QR
-
J. Demmel and K. Veselić, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl. 13:1204-1243 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 1204-1243
-
-
Demmel, J.1
Veselić, K.2
-
14
-
-
0000914013
-
The factorization of sparse symmetric indefinite matrices
-
I. S. Duff et al., The factorization of sparse symmetric indefinite matrices, IMA J. Numer. Anal. 11:181-204 (1991).
-
(1991)
IMA J. Numer. Anal.
, vol.11
, pp. 181-204
-
-
Duff, I.S.1
-
15
-
-
0012031747
-
LU decompositions of generalized diagonally dominant matrices
-
R. E. Funderlic, M. Neumann, and R. J. Plemmons, LU decompositions of generalized diagonally dominant matrices, Numer. Math. 40:57-59 (1982).
-
(1982)
Numer. Math.
, vol.40
, pp. 57-59
-
-
Funderlic, R.E.1
Neumann, M.2
Plemmons, R.J.3
-
16
-
-
0000620128
-
Preconditioners for indefinite systems arising in optimization
-
P. E. Gill, W. Murray, D. B. Ponceleón, and M. A. Saunders, Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl. 13:292-311 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 292-311
-
-
Gill, P.E.1
Murray, W.2
Ponceleón, D.B.3
Saunders, M.A.4
-
17
-
-
0026123179
-
Inertia-controlling methods for general quadratic programming
-
P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, Inertia-controlling methods for general quadratic programming, SIAM Rev. 33:1-36 (1991).
-
(1991)
SIAM Rev.
, vol.33
, pp. 1-36
-
-
Gill, P.E.1
Murray, W.2
Saunders, M.A.3
Wright, M.H.4
-
18
-
-
0026122066
-
What every computer scientist should know about floating-point arithmetic
-
D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Comput. Surveys 23:5-48 (1991).
-
(1991)
ACM Comput. Surveys
, vol.23
, pp. 5-48
-
-
Goldberg, D.1
-
20
-
-
0003306408
-
Analysis of the Cholesky decomposition of a semi-definite matrix
-
(M. G. Cox and S. Hammarling, Eds.), Clarendon Press
-
N. Higham, Analysis of the Cholesky decomposition of a semi-definite matrix, in Reliable Numerical Computation (M. G. Cox and S. Hammarling, Eds.), Clarendon Press, 1990.
-
(1990)
Reliable Numerical Computation
-
-
Higham, N.1
-
21
-
-
0031538118
-
Stability of the diagonal pivoting method with partial pivoting
-
N. Higham, Stability of the diagonal pivoting method with partial pivoting, SIAM J. Matrix Anal. Appl. 18:52-65 (1997).
-
(1997)
SIAM J. Matrix Anal. Appl.
, vol.18
, pp. 52-65
-
-
Higham, N.1
-
22
-
-
0042659923
-
-
Technical Report, Dept. of Mathematical Sciences, Northern Illinois Univ., Oct.
-
Y. P. Hong and C.-T. Pan, Rank-revealing QR Factorization and SVD, Technical Report, Dept. of Mathematical Sciences, Northern Illinois Univ., Oct. 1990.
-
(1990)
Rank-Revealing QR Factorization and SVD
-
-
Hong, Y.P.1
Pan, C.-T.2
-
28
-
-
85011438031
-
Perturbations of the eigenprojections of a factorized Hermitian matrix
-
I. Slapničar and K. Veselić, Perturbations of the eigenprojections of a factorized Hermitian matrix, Linear Algebra Appl 218:273-280 (1995).
-
(1995)
Linear Algebra Appl
, vol.218
, pp. 273-280
-
-
Slapničar, I.1
Veselić, K.2
-
29
-
-
0002090018
-
Condition numbers and equilibration of matrices
-
A. van der Sluis, Condition numbers and equilibration of matrices, Numer. Math. 14:14-23 (1969).
-
(1969)
Numer. Math.
, vol.14
, pp. 14-23
-
-
Van Der Sluis, A.1
-
30
-
-
38249010142
-
Rounding-error and perturbation bounds for the Cholesky and LDLT factorizations
-
J. Sun, Rounding-error and perturbation bounds for the Cholesky and LDLT factorizations, Linear Algebra Appl. 173:77-97 (1992).
-
(1992)
Linear Algebra Appl.
, vol.173
, pp. 77-97
-
-
Sun, J.1
-
31
-
-
21144467676
-
A Jacobi eigenreduction algorithm for definite matrix pairs
-
K. Veselić, A Jacobi eigenreduction algorithm for definite matrix pairs, Numer. Math. 64:241-269 (1993).
-
(1993)
Numer. Math.
, vol.64
, pp. 241-269
-
-
Veselić, K.1
-
32
-
-
21344486120
-
Floating-point perturbations of Hermitian matrices
-
K. Veselić and I. Slapničar, Floating-point perturbations of Hermitian matrices, Linear Algebra Appl. 195:81-116 (1993).
-
(1993)
Linear Algebra Appl.
, vol.195
, pp. 81-116
-
-
Veselić, K.1
Slapničar, I.2
-
33
-
-
84971922797
-
Interior methods for constrained optimization
-
(A. Iserles, Ed.), Cambridge U.P., New York
-
M. H. Wright, Interior methods for constrained optimization, in Acta Numerica (A. Iserles, Ed.), Cambridge U.P., New York, 1992.
-
(1992)
Acta Numerica
-
-
Wright, M.H.1
|