On the Factorization of Block-Tridiagonals without Storage Constraints
I tiakina i:
| I whakaputaina i: | Society for Industrial and Applied Mathematics. SIAM Journal on Scientific and Statistical Computing vol. 6, no. 1 (Jan 1985), p. 182 |
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| Kaituhi matua: | |
| I whakaputaina: |
Society for Industrial and Applied Mathematics
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| Ngā marau: | |
| Urunga tuihono: | Citation/Abstract Full Text - PDF |
| Ngā Tūtohu: |
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
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| Whakarāpopotonga: | In many programs solving difference equations, problem size is restricted by the number of available memory cells. A strategy has been developed to permit trade-offs between the number of floating point operations required and storage requirements for the solution of certain problems such as block tridiagonal systems of equations. This is done by recomputing some intermediate results instead of storing them. Reducing the storage to the square root of the current requirement will roughly double the number of computations. In theory, if $m$ is the order of each sub-matrix in the block tridiagonal matrix, one can solve any linear system with only $5m^2 + 1$ temporary storage cells. This method lends itself to efficient use on computers with parallel processing or vector processing architectures. On these computers the larger number of floating point operations is more than offset by the decrease in I/O and the increased percentage of vector operations made possible by this algorithm. |
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| ISSN: | 0196-5204 1064-8275 1095-7197 |
| DOI: | 10.1137/0906015 |
| Puna: | ABI/INFORM Global |