โ Scribed by Robert R. Hart
No coin nor oath required. For personal study only.
The eigenvalue problem is discussed from the viewpoint of computer mathematics and programming, with emphasis on applications to molecular spectroscopy. Particular mention is made of (a) the Danielevsky method of obtaining the coefcients of the characteristic polynomial of a matrix, (b) the Householder method of reducing a symmetric matrix to tridiagonal form, and (c) the Sturm method for obtaining the eigenvalues of a tridiagonal matrix or the roots of a polynomial. The Householder method forms the basis of the fastest and most stable procedure for obtaining eigenvalues. However, for matrices up to 9 X 9, the little-known Danielevsky method is considerably simpler and equally fast, as well as sufficiently stable for the secular matrices which arise from the Wilson FG matrix method. The Sturm method converges with complete certainty. For all three methods, complete FORTRAN computer programs are available, as are papers useful to those wishing to program these methods themselves.
๐ SIMILAR VOLUMES
In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is s