Mixed accelerated techniques for solving dense linear systems
نویسندگان
چکیده
The rounding-error analysis of Gaussian elimination shows that the method is stable only when the elements of the matrix do not grow excessively in the course of the reduction. Usually such growth is prevented by interchanging rows and columns of the matrix so that the pivot element is acceptably large. In this paper firstly we introduce the Boosting LU factorization method based on a rank one modification. In the next we propose an efficient algorithm based on an excisting algorithm that utilizes random transformation of the coefficient matrix to solve dense linear systems without pivoting. In the end we develop a mixed algorithm for solving dense linear systems.
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