论文信息 - Maximizing Functions of Rotations—Experiments Concerning Speed of Diagonalization of Symmetric Matrices Using Jacobi's Method

Maximizing Functions of Rotations—Experiments Concerning Speed of Diagonalization of Symmetric Matrices Using Jacobi's Method

We are interested in various methods which might be used with digital computing devices to maximize a function of a rotation. In particular, we are interested in the speed of convergence when elementary rotations (in the 2-plane of a pair of coordinate vectors as defined below) are used to generate the maximizing rotation. As a particular example we have chosen the Jacobi method of diagonalization of symmetric matrices [1], [9, pp. 280-285], in which the function to be maximized is the sum of the squares of the diagonal terms of the matrix

David A. Pope | C. Tompkins | C. Tompkins

[1] M. Lotkin. A set of test matrices , 1955 .

[2] R. T. Gregory. Computing eigenvalues and eigenvectors of a symmetric matrix on the ILLIAC , 1953 .

[3] C. Jacobi,et al. C. G. J. Jacobi's Gesammelte Werke: Über ein leichtes Verfahren, die in der Theorie der Sacularstorungen vorkommenden Gleichungen numerisch aufzulosen , 1846 .