A Digital Procedure for Use of the Method of Extensions and Restrictions of Quadratic Forms

摘要

This report describes the FORTRAN subroutine EROP that implements the method of 'Extensions and Restrictions of Operators' for calculation of rigorous lower bounds to eigenvalues of self-adjoint operators in separable Hilbert space, in particular, for lower bounds to frequencies of continuous linear elastic systems in free vibration. The method uses eigenvalues and eigenvectors of base problems to construct a matrix of which the eigenvalues are lower bounds to those of the self-adjoint operator. The inputs of EROP are double precision eigenvalues of the base problem and single precision matrices of inner products. Computations involving these eigenvalues are done in double precision and the elements of the matrix to be diagonalized are calculated in single precision rounded arithmetic. (Author)