By Klaus Appel
Communications of the ACM,
July 1962,
Vol. 5 No. 7, Page 381
10.1145/368273.368282
Comments
It is often desired to solve eigenvalue problems of the type (A - &lgr;1)C = 0 or (A - &lgr;B)C = 0 repeatedly for similar values of the matrix elements Aij, where A and B are Hermitean or real symmetric matrices. Among the various methods to find all eigenvalues and eigenvectors, Jacobi's method of two-dimensional rotations [1] has been very popular for its numerical stability, although it is comparatively time-consuming. The purpose of this note is to show how existing subroutines can be used to reduce substantially the computing time, if approximate eigenvectors are known from the previous solution of a similar problem.
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