Accession Number : AD0262708

Title :   ON THE CALCULATION OF ANALYTIC FUNCTIONS OF CYCLIC MATRICES

Corporate Author : MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS

Personal Author(s) : ABRAHAM,PHILLIP B. ; WEISS,GEORGE

Report Date : JUL 1961

Pagination or Media Count : 1

Abstract : IT IS THE PURPOSE OF THIS PAPER TO DISCUSS A METHOD FOR THE CALCULATION OF FUNCTIONS OF CYCLIC MATRICES, BOTH FOR THOSE ARISING FROM ONE DIMENSIONAL PROBLEMS AND THOSE ARISING FROM HIGHER DIMENSIONAL PROBLEMS. The technique is a generalization of the method in Lowdin, Pauncz, and de Heer (J. Math. Phys. 1:461, 1960) for the calculation of the inverse square root of a cyclic matrix. It is probably the only one of the methods men ioned by Lowdin, Pauncz, and de Heer which permits of a simple generalization to higher dimensions. Furthermore, the results are in such a form that approximate results are easily obtained when the conditions are such that these exist. The evaluation of functions of asymmetric cyclic matrices is also discussed since these present no more difficulty in theory than do symmetric cyclic matrices. (Author)

Descriptors :   *FUNCTIONS(MATHEMATICS), *MATRICES(MATHEMATICS), FOURIER ANALYSIS, INTEGRAL EQUATIONS, SERIES(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE