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Residual correction applied to a sequence of block tridiagonal matrices
Author(s) -
Brown R. Leonard
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620140711
Subject(s) - tridiagonal matrix , gaussian elimination , residual , tridiagonal matrix algorithm , block (permutation group theory) , mathematics , algorithm , matrix splitting , convergence (economics) , mathematical optimization , sequence (biology) , matrix (chemical analysis) , iterative method , gaussian , computer science , symmetric matrix , state transition matrix , combinatorics , computational chemistry , eigenvalues and eigenvectors , physics , chemistry , quantum mechanics , genetics , biology , economic growth , economics , composite material , materials science
The decomposition of a block tridiagonal matrix into the product of block lowe and upper matrices is described. The cost of solving a block tridiagonal system of equations is given and compared to profile gaussian elimination. The desirability of a less expensive method is coupled to physical intuition about a common problem of solving a slowly varying sequence of such systems to motivate an iterative method based on residual correction. The method is described and convergence criteria are derived. An expression of the cost is developed and is shown to compare favourably with decomposition in many cases. Problems and advantages in computer implementation of the method are discussed and results of tests of a particular implementation on a well‐known problem are given.