Sequential Linear Interpolation Correction Methods Used for Finding Zeros of Functions and Characteristic Polynomials of Matrices of a Special Form
Abstract
Computational schemes of the method of "correction of sequential linear interpolation (MCSLI)" are considered in this paper. MCSLI are used for finding zeros of nonlinear (including transcendental) functions, as well as zeros of characteristic polynomials of matrices of a special form, such as almost triangular (Hessenberg form), tridiagonal and others forms of matrices obtained, for example, by Givens or Householder methods from matrices of general form. The proposed computational schemes of MCSLI for cases of simple and multiple roots (including pathologically close roots) have a structural and functional similarity. MCSLI schemes designed to localize and improve multiple roots can also be used to localize a group of closely related roots consisting of simple roots and roots of different multiplicity (including pathologically close roots). The schemes of MCSLI have computational stability and a high convergence rate (the order of the convergence rate is approximately equal to two). Based on the results of computational experiments for MCSLI and other effective methods, the dependences of diagonalization time of matrices of a special form on the order of these matrices are obtained.
DOI 10.14258/izvasu(2018)1-16
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