On the Lánczos method for solving symmetric linear systems with several right-hand sides
作者： Youcef Saad
DOI: 10.1090/S0025-5718-1987-0878697-3
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摘要: This paper analyzes a few methods based on the Lanczos algorithm for solving large sparse symmetric linear systems with several right-hand sides. The examined are suitable situation when right sides not too different from one another, as is often case in time-dependent or parameter-dependent problems. We propose theoretical error bound approximation obtained projection process onto Krylov subspace generated processing previous side.
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sci-hub.se 参考文章(16)
Y. Saad, A. Sameh, A PARALLEL BLOCK STIEFEL METHOD FOR SOLVING POSITIVE DEFINITE SYSTEMS Elliptic Problem Solvers. pp. 405- 411 ,(1981) , 10.1016/B978-0-12-632620-8.50040-1
E. G. Carnoy, M. Geradin, On the practical use of the lanczos algorithm in finite element applications to vibration and bifurcation problems Springer, Berlin, Heidelberg. pp. 156- 176 ,(1983) , 10.1007/BFB0062100
Y. Saad, A. Sameh, Iterative methods for the solution of elliptic difference equations on multiprocessors Conpar 81. pp. 395- 413 ,(1981) , 10.1007/BFB0105132
Rati Chandra, Conjugate gradient methods for partial differential equations. Yale University. ,(1978)
B.N. Parlett, A new look at the Lanczos algorithm for solving symmetric systems of linear equations Linear Algebra and its Applications. ,vol. 29, pp. 323- 346 ,(1980) , 10.1016/0024-3795(80)90248-7
Youcef Saad, Practical Use of Some Krylov Subspace Methods for Solving Indefinite and Nonsymmetric Linear Systems SIAM Journal on Scientific and Statistical Computing. ,vol. 5, pp. 203- 228 ,(1984) , 10.1137/0905015
Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems Mathematics of Computation. ,vol. 37, pp. 105- 126 ,(1981) , 10.1090/S0025-5718-1981-0616364-6
C. C. Paige, M. A. Saunders, Solution of Sparse Indefinite Systems of Linear Equations SIAM Journal on Numerical Analysis. ,vol. 12, pp. 617- 629 ,(1975) , 10.1137/0712047
Horst D. Simon, The Lanczos algorithm with partial reorthogonalization Mathematics of Computation. ,vol. 42, pp. 115- 142 ,(1984) , 10.1090/S0025-5718-1984-0725988-X
Dianne P. O'Leary, The block conjugate gradient algorithm and related methods Linear Algebra and its Applications. ,vol. 29, pp. 293- 322 ,(1980) , 10.1016/0024-3795(80)90247-5