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Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods. (English) Zbl 0463.65025

65F15Eigenvalues, eigenvectors (numerical linear algebra)
Full Text: DOI
[1] Axelsson, O.: On preconditioning and convergence accelaration in sparse matrix problems. Cern 74-10 (1974) · Zbl 0354.65020
[2] Axelsson, O.: Solution of linear systems of equations: iterative methods. Sparse matrix techniques (1976) · Zbl 0334.65028
[3] Axelsson, O.: On preconditioned conjugate gradient methods. Cna-143 (1978)
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[9] Daniel, J. W.: The conjugate gradient method for linear and nonlinear operator equations. Ph.d. thesis (1965)
[10] Daniel, J. W.: The conjugate gradient method for linear and nonlinear operator equations. SIAM J. Numer. anal. 4, 10-26 (1967) · Zbl 0154.40302
[11] Eisenstat, S. C.; Elman, H.; Schultz, M. H.; Sherman, A. H.: Solving approximations to the convection diffusion equation. Proceedings of the society of petroleum engineers of the AIME (1979)
[12] S.C. Eisenstat, H. Elman, and M.H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations, unpublished. · Zbl 0524.65019
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[15] Fletcher, R.: Conjugate gradient methods for indefinite systems. Lecture notes in mathematics 506 (1976) · Zbl 0326.65033
[16] Golub, G. H.; Varga, R. S.: Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods. Numer. math. 3, 147-168 (1961) · Zbl 0099.10903
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[18] L.A. Hageman, F. Luk, and D.M. Young, On the equivalence of certain iterative acceleration methods, SIAM J. Numer. Anal., to appear. · Zbl 0472.65031
[19] Hageman, L. A.; Young, David M.: Applied iterative methods. (1981) · Zbl 0459.65014
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[21] Hestenes, Magnus R.: The conjugate-gradient method for solving linear systems. Numerical analysis (1956) · Zbl 0072.14102
[22] Lanczos, C.: An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. res. Nat. bur. Standards 45, 255-282 (1950)
[23] Lanczos, C.: Solution of systems of linear equations by minimized iterations. J. res. Nat. bur. Standards 49, 33-53 (1952)
[24] Manteuffel, T. A.: The tchebyshev iteration for nonsymmetric linear systems. Numer. math. 28, 307-327 (1977) · Zbl 0361.65024
[25] Reid, J. K.: On the method of conjugate gradients for the solution of large sparse systems of linear equations. Proceedings of the conference on large sparse sets of linear equations, 231-254 (1971)
[26] Reid, J. K.: The use of conjugate gradients for systems of linear equations possessing ”property A”. SIAM J. Numer. anal. 9, 325-332 (1972) · Zbl 0259.65037
[27] Richardson, L. F.: The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stresses in a masonry dam. Philos. trans. Roy. soc. London ser. A 210, 307-357 (1910) · Zbl 41.0871.04
[28] Vinsome, P. K. W.: ORTHOMIN, an iterative method for solving sparse sets of simultaneous linear equations. 4th symposium of numerical simulation of reservoir performance of the society of petroleum engineers of the AIME (1976)
[29] Widlund, O.: A Lanczos method for a class of nonsymmetric systems of linear equations. SIAM J. Numer. anal. 15, 801-812 (1978) · Zbl 0398.65030
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[32] Young, David M.; Jea, Kang C.: Some generalizations of conjugate gradient acceleration for nonsymmetrizable iterative methods. Cna-149 (1979)
[33] Young, David M.; Hayes, Linda; Jea, Kang C.: Conjugate gradient acceleration of iterative methods: part I, the symmetrizable case. Cna-162 (1980)
[34] Young, David M.; Jea, Kang C.: Conjugate gradient acceleration of iterative methods: part II, the nonsymmetrizable case. Cna-163 (1980)