ScholarLens Back to search
2005•Gongcheng shuxue xuebaoRequires access

The PE_κ Method for Solving Linear Algebraic Equations Derived from Discretizing Elliptic Partial Differential Equation with Periodic Boundary Conditions

Kaiyuan Zhang

Open publisher page 0 citations

Abstract

In this paper, we propose the PEκ method for solving a system of large scale linear algebraic equations with periodic block-tridiagonal matrix. Under the condition that the coefficient matrix is Hermitian positive definite, the solvability and convergence of the new method are proved, and the selection range for the parameter κ is given. For the example in this paper, the computation time of the PE2 method is only 50 percent of that of the SBGS method.

About this research paper

What this paper is about

In this paper, we propose the PEκ method for solving a system of large scale linear algebraic equations with periodic block-tridiagonal matrix. Under the condition that the coefficient matrix is Hermitian positive definite, the solvability and convergence of the new method are proved, and the selection range for the parameter κ is given. For the example in this paper, the computation time of the PE2 method is only 50 percent of that of the SBGS method.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we propose the PEκ method for solving a system of large scale linear algebraic equations with periodic block-tridiagonal matrix. Under the condition that the coefficient matrix is Hermitian positive definite, the solvability and convergence of the new method are proved, and the selection range for the parameter κ is given. For the example in this paper, the computation time of the PE2 method is only 50 percent of that of the SBGS method.

Key concepts: Mathematics, Coefficient matrix, Mathematical analysis, Elliptic partial differential equation, Tridiagonal matrix, Discretization, Matrix (chemical analysis), Boundary value problem

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The PE_κ Method for Solving Linear Algebraic Equations Derived from Discretizing Elliptic Partial Differential Equation with Periodic Boundary Conditions — Research Paper | ScholarLens