Article ID Journal Published Year Pages File Type
4629358 Applied Mathematics and Computation 2012 7 Pages PDF
Abstract

This paper proposes a divide and conquer algorithm for reconstructing a 2n2nth order Jacobi matrix J2nJ2n with a given n  th order leading principal submatrix JnJn and with all eigenvalues of J2nJ2n. This algorithm needs to compute the eigenvalues of the n  th order Jacobi matrix Jn+1,2n′ and the first components of the unit eigenvectors of Jn+1,2n′, where Jn+1,2n′=Jn+1,2n-βne1e1T. The method needs not to reconstruct the leading principal submatrix JnJn, and can avoid computing the coefficients of the characteristic polynomial for getting the eigenvalues of JnJn.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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