Accurate Computations Of Function Generalization Matrix Of Said-Ball-Vandermonde Basis

In this paper,two kinds of structural matrices of Said-Ball basis are studied: f-g-Said-Ball completely nonpositive matrix and inverse completely nonpositive matrix.Through proper selection of f and g in these two kinds of matrices,the eigenvalues,singular values and linear systems are calulated with high precision by using the new algorithm.First,the f-g-Said-Ball-Vandermonde completely nonpositive matrix and inverse completely nonpositive matrix are parameterized again.In the process of parameterization,the choice of f and g is different,which has certain influence on the calculation of high precision,so it should be make right choice for f and g.After parameterization,the bidiagonal decomposition of the matrix was realized.Then,the eigenvalue,singular value and linear system were numerically tested by the new algorithm and the traditional method.Finally,numerical experiments are carried out,the results of two methods are compared with results of Mathematica,so as to verify the algorithm's high precision calculation.