Title :
Modification of successive approximation method in generalized spectrum problems for quadratic matrix beams
Author :
Podlevskyi, B.M. ; Yaroskho, S.M.
Author_Institution :
Inst. for Appl. Problems of Mech. & Math., Acad. of Sci., Ukraine
Abstract :
The case of the eigenvalue problem of the quadratic matrix beam is proposed. The method permits one to calculate all eigenpairs of the matrix beam. With this aim, the generalized eigenvalue problem is reduced to a linear problem. Then, the modified successive approximations method is used for calculation of the eigenvalues and eigenvectors. This permits the use of the information obtained from the iterations, to obtain the first eigenpair and all the following ones more quickly. Some numerical examples are considered
Keywords :
approximation theory; eigenvalues and eigenfunctions; iterative methods; spectral analysis; eigenpairs; eigenvalue problem; eigenvalues; eigenvectors; generalized spectrum problems; iterations; linear problem; modified successive approximation method; quadratic matrix beams; Approximation methods; Educational institutions; Eigenvalues and eigenfunctions; Equations; Least squares methods; Mathematics; Physics; Polynomials; Vectors; Vibrations;
Conference_Titel :
Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 1998. DIPED-98. Proceedings of III International Seminar/Workshop on
Conference_Location :
Tbilisi
Print_ISBN :
966-02-0621-6
DOI :
10.1109/DIPED.1998.730948
