Symmetric Indefinite Line Equations Bbk And Relaxation In The Form Of The Bfp Algorithm And Special Matrix Analysis

Matrix computations and special matrix analysis have wide applications in com-putational mathematics, mathematic physics, economics, physics, biology and etc. This thesis studies the pivoting strategies of Cholesky factorization for symmetric indefinite matrices, the estimation of spectral radius for nonnegative irreducible ma-trices and the estimation for the elements of the inverse of the tridiagonal matrices.In the second chapter, we discuss the relaxed forms of the BBK algorithm and the FBP algorithm for solving the symmetric indefinite systems with linear equations directly and stably. These two algorithms adopt flexible pivot slecting strategy, which can find a pivot fast and make‖L‖∞bounded in the LDL~T factorization.Based on the fact that a tridiagonal matrix can be factorized as two special matrices, we discuss the estimation for the inverse of the tridiagonal matrices in chapter three. And we propose a new method to estimate the elements efficiently.In the fourth chapter, a new method for esitmating the upper and lower bounds for the spectral radius of a nonnegative matrix is proposed. The presented numerical examples show the effectiveness of this method.