تقرير
Speeding up Krylov subspace methods for computing f(A)b via randomization
| العنوان: | Speeding up Krylov subspace methods for computing f(A)b via randomization |
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| المؤلفون: | Cortinovis, Alice, Kressner, Daniel, Nakatsukasa, Yuji |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65F60 |
| الوصف: | This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed by forming an orthonormal basis of the Krylov subspace using the Arnoldi method. In this work, we propose to compute (non-orthonormal) bases in a faster way and to use a fast randomized algorithm for least-squares problems to compute the compression of A onto the Krylov subspace. We present some numerical examples which show that our algorithms can be faster than the standard Arnoldi method while achieving comparable accuracy. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2212.12758Test |
| رقم الانضمام: | edsarx.2212.12758 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |