TY - JOUR

T1 - Rational approximation preconditioners for sparse linear systems

AU - Guillaume, Philippe

AU - Saad, Yousef

AU - Sosonkina, Masha

PY - 2003/9/15

Y1 - 2003/9/15

N2 - This paper presents a class of preconditioning techniques which exploit rational function approximations to the inverse of the original matrix. The matrix is first shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner for the original matrix. Since the incomplete factorization is made on a shifted matrix, a good LU factorization is obtained without allowing much fill-in. The result needs to be extrapolated to the nonshifted matrix. Thus, the main motivation for this process is to save memory. The method is useful for matrices whose incomplete LU factorizations are poor, e.g., unstable.

AB - This paper presents a class of preconditioning techniques which exploit rational function approximations to the inverse of the original matrix. The matrix is first shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner for the original matrix. Since the incomplete factorization is made on a shifted matrix, a good LU factorization is obtained without allowing much fill-in. The result needs to be extrapolated to the nonshifted matrix. Thus, the main motivation for this process is to save memory. The method is useful for matrices whose incomplete LU factorizations are poor, e.g., unstable.

KW - Incomplete LU factorization

KW - Matrix diagonal shifting

KW - Padé approximation

KW - Preconditioning

KW - Rational approximation

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U2 - 10.1016/S0377-0427(03)00480-1

DO - 10.1016/S0377-0427(03)00480-1

M3 - Article

AN - SCOPUS:0141737699

VL - 158

SP - 419

EP - 442

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -