Inverses of Block Tridiagonal Matrices and Rounding Errors
Based on URV-decomposition in Stewart [An updating algorithm for subspace tracking, IEEE Trans. Signal Processing, 40 (1992): 1535--1541] and the result of Mehrmann [Divide and conquer methods for block tridiagonal systems, \emph{Parallel Comput.}, 19 (1993): 257--279], inverses of block tridiagonal...
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| Published in: | Bulletin of the Malaysian Mathematical Sciences Society Vol. 34; no. 2 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Springer Nature B.V
01.01.2011
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| Subjects: | |
| ISSN: | 0126-6705, 2180-4206 |
| Online Access: | Get full text |
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| Summary: | Based on URV-decomposition in Stewart [An updating algorithm for subspace tracking, IEEE Trans. Signal Processing, 40 (1992): 1535--1541] and the result of Mehrmann [Divide and conquer methods for block tridiagonal systems, \emph{Parallel Comput.}, 19 (1993): 257--279], inverses of block tridiagonal matrices are presented. The computational complexity of the proposed algorithm is less than that of the Block Gaussian-Jordan Elimination method when the orders of the matrices are not less than 100. Expressions for the rounding errors incurred during the process of the computation of the inverses of block tridiagonal matrices are also considered. Moreover, from the experiment, it shows that the norms of the errors generated from the Block Gaussian-Jordan Elimination method are larger than those of the proposed algorithm. 2010 Mathematics Subject Classification: 65F05, 65G50, 65Y20. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0126-6705 2180-4206 |