Stable Computation of Generalized Matrix Functions via Polynomial Interpolation.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS(2019)

引用 11|浏览40
暂无评分
摘要
Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on Chebyshev interpolation. The method is matrix free and requires no orthogonalization and minimal additional storage. Comparisons against existing approaches based on Lanczos bidiagonalization demonstrate the competitiveness of our approach. We prove that our method is backward stable by generalizing the proof of the backward stability of Clenshaw's algorithm to the matrix case.
更多
查看译文
关键词
generalized matrix functions,Chebyshev polynomials,Clenshaw's algorithm,graph theory
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要