The stability of LU-decompositions of block tridiagonal matrices

R.M.M. Mattheij

doi:10.1017/S0004972700021432

The stability of LU-decompositions of block tridiagonal matrices

R.M.M. Mattheij

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

An investigation is made of the stability of block LU-decomposition of matrices A arising from boundary value problems of differential equations, in particular of ordinary differential equations with separated boundary conditions. It is shown that for such matrices the pivotal growth can be bounded by constants of the order of ‖A‖ and, if solution space is dichotomic, often by constants of order one. Furthermore a method to estimate the growth of the pivotal blocks is given. A number of examples support the analysis.

Original language	English
Pages (from-to)	177-205
Journal	Bulletin of the Australian Mathematical Society
Volume	29
Issue number	2
DOIs	https://doi.org/10.1017/S0004972700021432
Publication status	Published - 1984

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title = "The stability of LU-decompositions of block tridiagonal matrices",

abstract = "An investigation is made of the stability of block LU-decomposition of matrices A arising from boundary value problems of differential equations, in particular of ordinary differential equations with separated boundary conditions. It is shown that for such matrices the pivotal growth can be bounded by constants of the order of ‖A‖ and, if solution space is dichotomic, often by constants of order one. Furthermore a method to estimate the growth of the pivotal blocks is given. A number of examples support the analysis.",

author = "R.M.M. Mattheij",

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AU - Mattheij, R.M.M.

PY - 1984

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N2 - An investigation is made of the stability of block LU-decomposition of matrices A arising from boundary value problems of differential equations, in particular of ordinary differential equations with separated boundary conditions. It is shown that for such matrices the pivotal growth can be bounded by constants of the order of ‖A‖ and, if solution space is dichotomic, often by constants of order one. Furthermore a method to estimate the growth of the pivotal blocks is given. A number of examples support the analysis.

AB - An investigation is made of the stability of block LU-decomposition of matrices A arising from boundary value problems of differential equations, in particular of ordinary differential equations with separated boundary conditions. It is shown that for such matrices the pivotal growth can be bounded by constants of the order of ‖A‖ and, if solution space is dichotomic, often by constants of order one. Furthermore a method to estimate the growth of the pivotal blocks is given. A number of examples support the analysis.

U2 - 10.1017/S0004972700021432

DO - 10.1017/S0004972700021432

M3 - Article

SN - 0004-9727

VL - 29

SP - 177

EP - 205

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

The stability of LU-decompositions of block tridiagonal matrices

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