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

내부점 방법에서 촐레스키 분해의 수치적 안정성

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.