Randomized low-rank approximation for symmetric indefinite matrice
The Nystr¨om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In this work, we first identify the main challenges in finding a...
| Glavni autori: | , |
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| Format: | Journal article |
| Jezik: | English |
| Izdano: |
Society for Industrial and Applied Mathematics
2023
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| Sažetak: | The Nystr¨om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In this work, we first identify the main challenges in finding a Nystr¨om approximation to symmetric indefinite matrices. We then prove the existence of a variant that overcomes the instability, and establish relative-error nuclear norm bounds of the resulting approximation that hold when the singular values decay rapidly. The analysis naturally leads to a practical algorithm, whose robustness is illustrated with experiments. |
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