A Note on the Solution of Circulant Real Linear Systems and its Sensitivity Analysis

TL;DR

This paper presents a practical FFT-based method for solving circulant real linear systems and analyzes how strict diagonal dominance influences solution sensitivity, aiding theoretical understanding.

Contribution

It introduces a fast FFT-based solution method for circulant systems and establishes diagonal dominance as a condition for sign consistency in sensitivity analysis.

Findings

FFT provides an efficient solution approach.

Diagonal dominance ensures sign stability.

Method is useful for theoretical analysis.

Abstract

Employing the Fast Fourier Transform we propose a ready-to-use solution to circulant real linear systems of equations, particularly useful when a broader theoretical analysis is involved. We also show that strict diagonal dominance of the matrix of coefficients is a sufficient condition for sign consistency between solutions and parameters in sensitivity analysis. Keywords: Circulant matrix, Real linear system of equations, Circulant structure, FFT, Sensitivity Analysis, Strict Diagonal Dominance.