Approximate sparsity patterns for the inverse of a matrix and preconditioning

Thomas Huckle

doi:10.1016/S0168-9274(98)00117-2

Approximate sparsity patterns for the inverse of a matrix and preconditioning

Thomas Huckle

Default

Research output: Contribution to journal › Conference article › peer-review

96 Scopus citations

Abstract

This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A^-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A^-1 are developed using the characteristic polynomials and the Neumann series associated with A and A^T A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.

Original language	English
Pages (from-to)	291-303
Number of pages	13
Journal	Applied Numerical Mathematics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/S0168-9274(98)00117-2
State	Published - Jun 1999
Event	Proceedings of the 1997 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics - Berlin, Ger Duration: 24 Aug 1997 → 29 Aug 1997

Access to Document

10.1016/S0168-9274(98)00117-2

Cite this

@article{8053b960abe64afbb51e87c6e69b85a7,

title = "Approximate sparsity patterns for the inverse of a matrix and preconditioning",

abstract = "This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A-1 are developed using the characteristic polynomials and the Neumann series associated with A and AT A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.",

author = "Thomas Huckle",

year = "1999",

month = jun,

doi = "10.1016/S0168-9274(98)00117-2",

language = "English",

volume = "30",

pages = "291--303",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier B.V.",

number = "2",

note = "Proceedings of the 1997 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics ; Conference date: 24-08-1997 Through 29-08-1997",

}

TY - JOUR

T1 - Approximate sparsity patterns for the inverse of a matrix and preconditioning

AU - Huckle, Thomas

PY - 1999/6

Y1 - 1999/6

N2 - This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A-1 are developed using the characteristic polynomials and the Neumann series associated with A and AT A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.

AB - This study addresses a general sparse matrix A. Different strategies for choosing a-priori an approximate sparsity structure of A-1 are compared. Following this, heuristic methods to find good and sparse approximate patterns for A-1 are developed using the characteristic polynomials and the Neumann series associated with A and AT A. Further, the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse are exactly determined.

UR - http://www.scopus.com/inward/record.url?scp=0033149565&partnerID=8YFLogxK

U2 - 10.1016/S0168-9274(98)00117-2

DO - 10.1016/S0168-9274(98)00117-2

M3 - Conference article

AN - SCOPUS:0033149565

SN - 0168-9274

VL - 30

SP - 291

EP - 303

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 2

T2 - Proceedings of the 1997 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics

Y2 - 24 August 1997 through 29 August 1997

ER -

Approximate sparsity patterns for the inverse of a matrix and preconditioning

Abstract

Access to Document

Other files and links

Fingerprint

Cite this