[1] Arnoldi, W.:
The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quart. Appl. Math. 9 (1951), 17–29.
MR 0042792 |
Zbl 0042.12801
[3] Axelsson, O.: Optimal preconditioners based on rate of convergence estimates for the conjugate gradient method. LN of IMAMM 99 (eds. Míka, S., Brandner, M.), Univ. of West Bohemia, Pilsen 1999, 5–56.
[4] Axelsson, O., Barker, V. A.:
Finite element solution of boundary value problems. Theory and computation. Academic Press, New York 1984.
MR 0758437 |
Zbl 0537.65072
[5] Beckermann, B., Kuijlaars, A. B. J.:
Superlinear convergence of conjugate gradients. SIAM J. Numer. Anal. 39 (2001), 300–329.
MR 1860727 |
Zbl 0997.65058
[6] Benzi, M., Tůma, M.:
A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comput. 19 (1998), 968–994.
MR 1616710
[7] Brandts, J.: Explanation of a phenomenon witnessed in pre-processed GMRES. ENUMATH 99 — Proc. of the 3rd European Conf. on Numer. Math. and Advanced Applications, Jyväskylä, Finland 1999, ed. by Neittaanmäki, P. et al., World Scientific, Singapore 2000, 440–447.
[8] Brandts, J.: Riccati algorithms for eigenvalues and invariant subspaces of large and sparse matrices. Accepted by Linear Algebra Appl. in 2001.
[9] Coppersmith, D., Winograd, S.:
Matrix multiplication via arithmetic progression. J. Symbolic Comput. 9 (1990), 251–280.
MR 1056627
[10] Daniel, J. W.:
The conjugate gradient method for linear and nonlinear operator equations. SIAM J. Numer. Anal. 4 (1967), 10–26.
MR 0217987 |
Zbl 0154.40302
[11] Golub, G. H., Loan, Ch. F. van: Matrix computation. The John Hopkins Univ. Press, Baltimore 1984.
[12] Hestenes, M. R., Stiefel, E.:
Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952), 409–436.
MR 0060307 |
Zbl 0048.09901
[13] Jennings, A.:
Influence of the eigenvalue spectrum on the convergence rate of the conjugate gradient method. J. Inst. Maths Applics 20 (1977), 61–72.
MR 0451658 |
Zbl 0364.65028
[14] Kaniel, S.:
Estimates for some computational techniques in linear algebra. Math. Comp. 20 (1966), 369–378.
MR 0234618
[15] Křížek, M., Neittaanmäki, P.:
Finite Element Approximation of Variational Problems and Applications. Longman Scientific & Technical, Harlow; John Wiley & Sons, New York 1990.
MR 1066462
[16] Křížek, M., Neittaanmäki, P.:
Mathematical and Numerical Modelling in Electrical Engineering: Theory and Applications. Kluwer Academic Publishers, Dordrecht 1996.
MR 1431889
[17] Křížek, M., Segeth, K.: Numerické modelování problémů elektrotechniky. Karolinum, Praha 2001.
[18] Lanczos, C.:
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Standards 45 (1950), 255–282.
MR 0042791
[19] Lanczos, C.:
Solution of systems of linear equations by minimized iterations. J. Res. Nat. Bur. Standards 49 (1952), 33–53.
MR 0051583
[20] Saad, Y., Schultz, M. H.:
GMRES: a generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986), 856–869.
MR 0848568
[21] Simoncini, V.:
A stabilized QMR version of block BiCG. SIAM J. Matrix Anal. Appl. 18 (1997), 419–434.
MR 1437340 |
Zbl 0872.65024
[22] Simoncini, V.:
On the convergence of restarted Krylov subspace methods. SIAM J. Matrix Anal. Appl. 22 (2000), 430–452.
MR 1780193 |
Zbl 0969.65023
[23] Sluis, A. van der, Vorst, H. van der:
The rate of convergence of conjugate gradients. Numer. Math. 48 (1986), 543–560.
MR 0839616
[24] Sorensen, D. C.:
Implicit application of polynomial filters in a $k$-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13 (1992), 357–385.
MR 1146670 |
Zbl 0763.65025
[26] Strassen, V.:
Algebraic complexity theory. Handbook of Theoretical Computer Science, Vol. A (ed. van Leeuwen, J.), Elsevier, Amsterdam 1990, 634–672.
MR 1127177 |
Zbl 0900.68247
[27] Vorst, H. van der:
Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13 (1992), 631–644.
MR 1149111 |
Zbl 0761.65023
[28] Verzuh, F. M.:
The solution of simultaneous linear equations with the aid of the 602 calculating punch. Math. Comp. (Math. Tables and other Aids to Computation) 3 (1949), 453–462.
MR 0030816
[29] Zítko, J.:
Combining the preconditioned conjugate gradient method and a matrix iterative method. Appl. Math. 41 (1996), 19–39.
MR 1365137
[30] Zowe, J.:
Nondifferentiable optimization — a motivation and short introduction in the subgradient and the bundle concept. ASI Proc. Comp. Math. Progr. 1985, 323–356.
MR 0820049