Forming a symmetric, unreduced, tridiagonal matrix with a given spectrum

Luca Dieci; Alessandro Pugliese

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arXiv · 2311.02677

Forming a symmetric, unreduced, tridiagonal matrix with a given spectrum

Luca Dieci·Alessandro Pugliese

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Abstract

Given a set of $n$ distinct real numbers, our goal is to form a symmetric, unreduced, tridiagonal, matrix with those numbers as eigenvalues. We give an algorithm which is a stable implementation of a naive algorithm forming the characteristic polynomial and then using a technique of Schmeisser.

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Luca Dieci, Alessandro Pugliese. 2023-11-05. Forming a symmetric, unreduced, tridiagonal matrix with a given spectrum. https://arxiv.org/abs/2311.02677

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