Determination of eigenvalues of large structural systems in an arbitrarily specified range
Maharaj K. Kaul · International Journal for Numerical Methods in Engineering · 1977
Abstract For a large structural system of small bandwidth a technique combining linear interpolation on the characteristic polynomial and suppression of its previously determined roots by deflation can be used to determine its eigenvalues. The eigenvalues, however, have to be found in order, beginning from either the lowest (or the highest) to obtain monotonic convergence to the polynomial roots. A method which eliminates this restriction is presented in this paper. If eigenvalues greater than a are desired, the method, in essence, consists of modifying the deflation procedure to suppress all the eigenvalues smaller than a without actually determining them. Some consequences of the procedure developed in this paper are also presented and it is shown that the standard deflation technique is a special case of this procedure. The method has been applied to a wide range of problems with success and considerable saving in computation time.