Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Calculating a function of a matrix with a real spectrum (2105.15173v1)

Published 31 May 2021 in math.NA, cs.NA, and math.SP

Abstract: Let $T$ be a square matrix with a real spectrum, and let $f$ be an analytic function. The problem of the approximate calculation of $f(T)$ is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that $T$ is triangular and its diagonal entries $t_{ii}$ are arranged in increasing order. To avoid calculations using the differences $t_{ii}-t_{jj}$ with close (including equal) $t_{ii}$ and $t_{jj}$, it is proposed to represent $T$ in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the $f(T)$ entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform scalar operations (such as the building of interpolating polynomials) with an enlarged number of decimal digits.

Summary

We haven't generated a summary for this paper yet.