# Spectrum-adapted Polynomial Approximation for Matrix Functions.

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)（2019）

摘要

We propose and investigate two new methods to approximate f(A)b for large, sparse, Hermitian matrices A. Computations of this form play an important role in numerous signal processing and machine learning tasks. The main idea behind both methods is to first estimate the spectral density of 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(A)b at lower polynomial orders, and for matrices A with a large number of distinct interior eigenvalues and a small spectral width.

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关键词

Matrix function,spectral density estimation,polynomial approximation,orthogonal polynomials,graph spectral filtering,weighted least squares polynomial regression

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