| Autor: |
Fan, Li, Shuman, David I, Ubaru, Shashanka, Saad, Yousef |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We propose and investigate two new methods to approximate $f({\bf A}){\bf b}$ for large, sparse, Hermitian matrices ${\bf A}$. The main idea behind both methods is to first estimate the spectral density of ${\bf A}$, and then find polynomials of a fixed order that better approximate the function $f$ on areas of the spectrum with a higher density of eigenvalues. Compared to state-of-the-art methods such as the Lanczos method and truncated Chebyshev expansion, the proposed methods tend to provide more accurate approximations of $f({\bf A}){\bf b}$ at lower polynomial orders, and for matrices ${\bf A}$ with a large number of distinct interior eigenvalues and a small spectral width. |
| Databáze: |
arXiv |
| Externí odkaz: |
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