Stability of the Lanczos algorithm on matrices with regular spectral distributions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929339776368640 |
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| author | Chen, Tyler Trogdon, Thomas |
| author_facet | Chen, Tyler Trogdon, Thomas |
| contents | We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be upgraded to a forward stability result when the reference measure has a density supported on a single interval with square root behavior at the endpoints. Our analysis implies the Lanczos algorithm run on many large random matrix models is in fact forward stable, and hence nearly deterministic, even when computations are carried out in finite precision arithmetic. Since the Lanczos algorithm is not forward stable in general, this provides yet another example of the fact that random matrices are far from "any old matrix", and care must be taken when using them to test numerical algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14842 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of the Lanczos algorithm on matrices with regular spectral distributions Chen, Tyler Trogdon, Thomas Numerical Analysis 42C05, 65F10, 65F60 We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be upgraded to a forward stability result when the reference measure has a density supported on a single interval with square root behavior at the endpoints. Our analysis implies the Lanczos algorithm run on many large random matrix models is in fact forward stable, and hence nearly deterministic, even when computations are carried out in finite precision arithmetic. Since the Lanczos algorithm is not forward stable in general, this provides yet another example of the fact that random matrices are far from "any old matrix", and care must be taken when using them to test numerical algorithms. |
| title | Stability of the Lanczos algorithm on matrices with regular spectral distributions |
| topic | Numerical Analysis 42C05, 65F10, 65F60 |
| url | https://arxiv.org/abs/2302.14842 |