The complexity of accurate floating point computation
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arXiv
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| Format: | Preprint |
| Published: |
2003
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| _version_ | 1866912655483076608 |
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| author | Demmel, James |
| author_facet | Demmel, James |
| contents | Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational expressions as entries. More precisely, {\em accuracy} means the relative error in the output must be less than one (no matter how tiny the output is), and {\em efficiency} means that the algorithm runs in polynomial time. Our goal is challenging because our accuracy demand is much stricter than usual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0305004 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | The complexity of accurate floating point computation Demmel, James Numerical Analysis 65F, 65G50, 65Y20, 68Q25 Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational expressions as entries. More precisely, {\em accuracy} means the relative error in the output must be less than one (no matter how tiny the output is), and {\em efficiency} means that the algorithm runs in polynomial time. Our goal is challenging because our accuracy demand is much stricter than usual. |
| title | The complexity of accurate floating point computation |
| topic | Numerical Analysis 65F, 65G50, 65Y20, 68Q25 |
| url | https://arxiv.org/abs/math/0305004 |