Algorithms for the solution of the generalized eigenvalue problem - Bohte, Zvonimir (Informatica (Ljubljana), 1982)
In this paper we deal with generalized eigenvalue problem of matrix ?$A(z)$? with elements which are polynomials of ?$z$?. The well known iterative methodsof Muller, Newton and Laguerre for finding the zeros of function ?$f(z) = {\rm det} A(z)$? are analyzed. Decompositions of the matrix ?$A(z)$? and its derivatives are introduced in order to simplify the computations of the values of ?$f(z)$? and its first and second derivatives. Comparative analysis gives some indicators about the rate of convergence, computer time and accuracy of the computed eigenvalues for each of the method used. The analysed methods proved generally to be stable, economical and easily applicable. Fortran subroutines and an example of main calling programme are added for Muller's and Laguerre's method which proved tyo be more efficient than Newton's.
Keywords: derivative of the determinant; generalized eigenvalue problems; Laguerre's method; Laguerrova metoda; matematika; mathematics; Mullerjeva metoda; Muller's method; Newtonova metoda; Newton's method; numerical analysis; numerična analiza; odvod determinante; posplošeni problem lastnih vrednosti