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Monotonicity of the Spectral Radius of Modified Incomplete Gauss-Seidel Iteration for Z-matrices

Zhenyue Zhang

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Abstract

In this paper, we consider the parameter vector α of the modified incomplete Gauss-Seidel method (MIGS). We prove that the spectral radius function ρ_α of the iterative matrix T_αof MIGS withα is strictly monotonic decreasing at the condition of 0≤α≤e if the classical Gauss-Seidel method converges for a Z-matrix.

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What this paper is about

In this paper, we consider the parameter vector α of the modified incomplete Gauss-Seidel method (MIGS). We prove that the spectral radius function ρ_α of the iterative matrix T_αof MIGS withα is strictly monotonic decreasing at the condition of 0≤α≤e if the classical Gauss-Seidel method converges for a Z-matrix.

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Available abstract

In this paper, we consider the parameter vector α of the modified incomplete Gauss-Seidel method (MIGS). We prove that the spectral radius function ρ_α of the iterative matrix T_αof MIGS withα is strictly monotonic decreasing at the condition of 0≤α≤e if the classical Gauss-Seidel method converges for a Z-matrix.

Key concepts: Spectral radius, Gauss–Seidel method, Monotonic function, Mathematics, Matrix (chemical analysis), RADIUS, Applied mathematics, Iterative method

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