Name
Abstract | ||
|---|---|---|
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. |
Year | Venue | Field |
|---|---|---|
2018 | ICASSP | Applied mathematics,Mathematical optimization,Spectral density estimation,Lanczos resampling,Orthogonal polynomials,Polynomial,Matrix (mathematics),Computer science,Matrix function,Hermitian matrix,Eigenvalues and eigenvectors |
DocType | Volume | Citations |
Journal | abs/1808.09506 | 1 |
PageRank | References | Authors |
0.37 | 15 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Li Fan | 1 | 17 | 4.73 |
| David I. Shuman | 2 | 472 | 22.38 |
| shashanka ubaru | 3 | 58 | 8.97 |
| Yousef Saad | 4 | 1940 | 254.74 |