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

2023/11/05 by Luca Dieci, Dieci, Luca, Alessandro Pugliese +1
Computer Science · Engineering · Mathematics · #15A18 #65F18 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2311.02677

openalex publication_date 2023/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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