Use of modified bisection algorithm for the vibrating beam problem
David John Evans · Communications in Applied Numerical Methods · 1985
Abstract In this paper, the implementation of the incomplete Sturm sequence evaluation of Evans et al. 2 is considered for the determination of the eigenvalues of a symmetric quindiagonal matrix A which occurs in vibrating beam problems. The method based on triangularization by elementary stabilized matrices involving the application of the bisection method for quindiagonal matrices is fully described in Sentance and Cliff, 3 and therefore only the changes to the proposed method in order to obtain high efficiency when dealing with several of the lowest or highest eigenvalues of quindiagonal matrices are discussed. The paper concludes with the FORTRAN program and the supporting numerical evidence.