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Abstract: We propose a method for the solution of linear systems AX = B where A is a large, possibly sparse, nonsymmetric matrix of order n, and B is an arbitrary rectangular matrix of order n \Theta s with s of moderate size. The method uses a single Krylov subspace per step as a generator of approximations, a projection process, and a Richardson acceleration technique. It thus combines the advantages of recent hybrid methods with those for solving symmetric systems with multiple right-hand sides.... (Update)
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...of the other linear systems are projected onto this Krylov subspace. The process is repeated until convergence; see [15] 4] 11] [18] and [20] The popular Lanczos method ( 12] 1] for a single right hand side linear system is an oblique projection method onto a...
...nd the best solution within that subspace. De ation is used to remove vectors that become linearly dependent. Seed algorithms [3] [21] form a Krylov subspace using one of the right hand sides and then nd the best solution for each of the m problems within that subspace....
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BibTeX entry: (Update)
V. SIMONCINI AND E. GALLOPOULOS,An iterative method for nonsymmetric systems with multiple right-hand sides, SIAM J. Sci. Comput., 16(4):917--933, July 1995. http://citeseer.ist.psu.edu/simoncini95iterative.html More
@article{ simoncini95iterative,
author = "V. Simoncini and E. Gallopoulos",
title = "An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides",
journal = "SIAM Journal on Scientific Computing",
volume = "16",
number = "4",
pages = "917--933",
year = "1995",
url = "citeseer.ist.psu.edu/simoncini95iterative.html" }
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