V-cycle optimal convergence for DCT-III matrices

TL;DR

This paper proves that a multigrid V-cycle method converges at a constant rate for DCT-III matrices generated by polynomial symbols, with numerical examples confirming the theoretical results.

Contribution

It establishes size-independent convergence of the V-cycle multigrid method for DCT-III matrices, a novel theoretical result in this matrix class.

Findings

Convergence rate is constant regardless of matrix size.

Numerical examples validate theoretical convergence properties.

Multigrid method effectively solves differential and integral equation discretizations.

Abstract

The paper analyzes a two-grid and a multigrid method for matrices belonging to the DCT-III algebra and generated by a polynomial symbol. The aim is to prove that the convergence rate of the considered multigrid method (V-cycle) is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are considered to illustrate the claimed convergence properties.