Sumop. A Digital Implementation of the Method of Sums of Resolvable Operators

摘要

This report describes SUMOP, a FORTRAN subroutine that implements the method of sums of resolvable operators. This procedure is used to calculate rigorous lower bounds for eigenvalues of certain self-adjoint operators in Hilbert space and, in particular, lower bounds for the frequencies of free vibration of some continuous linear elastic systems. SUMOP employs eigenvalues and eigenvectors of part problems to construct a matrix, the eigenvalues of which yield lower bounds to those of the self-adjoint operator. The inputs to SUMOP are double precision eigenvalues and single precision matrices of inner products of eigenvectors of the part problems. Computations involving the eigenvalues are done in double precision and rounded down to single precision prior to forming the matrix to be diagonalized. Calculations involved in the formation of this matrix are done in single precision rounded arithmetic. (Author)