التفاصيل البيبلوغرافية
| العنوان: |
RANDOMIZED LOW-RANK APPROXIMATION FOR SYMMETRIC INDEFINITE MATRICES. |
| المؤلفون: |
YUJI NAKATSUKASA, TAEJUN PARK |
| المصدر: |
SIAM Journal on Matrix Analysis & Applications; 2023, Vol. 44 Issue 3, p1370-1392, 23p |
| مصطلحات موضوعية: |
SYMMETRIC matrices, LINEAR algebra |
| مستخلص: |
The Nyström method is a popular choice for finding a low-rank approximation to a symmetric positive semidefinite 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 Nyström 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. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
