Analysis of projection methods for solving linear systems with multiple right-hand sides. (English) Zbl 0888.65033

Chan, Tony F.; Wan, W. L.

SIAM J. Sci. Comput. 18, No. 6, 1698-1721 (1997).

A class of Krylov projection methods is analyzed to solve the linear system \(AX= B\), where \(A\) is a symmetric positive definite matrix, and \(B\) is a multiple of the right-hand sides. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the conjugate gradient method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The numerical properties of the method are examined and a block extension is introduced.

Reviewer: F.Szidarovszky (Tucson)

MSC:

65F10	Iterative numerical methods for linear systems
65Y20	Complexity and performance of numerical algorithms

Keywords:

multiple right-hand sides; Lanczos algorithm; conjugate gradient method; Krylov projection methods; Krylov subspace