Re-parametrization And High-accuracy Computations Of Several Classes Of Structured Matrices

In numerical algebra,the main problem is that high precision is not determined by matrix elements,and high precision numerical results are our ideal goal.For totally nonpositive matrix(sub formula nonpositive)and inversely totally nonpositive matrix(its inverse is totally nonpositive matrix),the double diagonal decomposition is carried out by Neville elimination method,and the parameters of these two kinds of matrices are calculated with high relative accuracy,the matrix is parameterized,Then an algorithm is designed to calculate these two kinds of matrices.Finally,some numerical experiments are given.The experimental results show that the algorithm is effective.The specific arrangement of this paper is as follows:In chapter one,it describes the correlation theory of TNP matrix and inverse TNP matrix and the correlation results of high relative accuracy,and explains the symbols used in this paper,and then describes the correlation properties of Neville elimination method and fg-vandermonde matrix.In chapter two,we find two kinds of functions f(x)and g(x),and then get the high relative accuracy double diagonal decomposition of fg-Vandermonde like matrix by Neville elimination method,and calculate the parameters with high relative accuracy,then design the algorithm of high relative accuracy singularvalue calculation.The last two numerical examples are given to determine whether the algorithm is high relative accuracy.In Chapter three,the subformula of generalized fg-vandermonde matrix is given,and then when the function f(t)/g(t)=t,and the parameters are calculated with high relative accuracy,then the algorithm for calculating eigenvalues and singular values with high relative accuracy is designed.