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1999•Journal of Korean Institute of Industrial EngineersRequires access

Numerical Stability of Cholesky Factorization in Interior Point Methods for Linear Programming

Tong-Ryeol Seol, Myeong-Ki Seong, Jae-Geun Ahn, Soon-Dal Park

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Abstract

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

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What this paper is about

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

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Available abstract

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

Key concepts: Cholesky decomposition, Incomplete Cholesky factorization, Minimum degree algorithm, Factorization, Incomplete LU factorization, Linear programming, Stability (learning theory), Dixon's factorization method

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