DETERMINANTAL EVALUATION OF EIGENVALUES.
AEROSPACE RESEARCH LABS OFFICE OF AEROSPACE RESEARCH WRIGHT-PATTERSON AFB OHIO
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The numerical determination of the eigenvalues of a matrix consists of two phases one, the isolation of the eigenvalues and, two, the calculation proper. The report concerns itself with the second phase and assumes that the first, probably more difficult, phase has been accomplished. The method presented requires the lower and upper bounds of the distinct real eigenvalues of a real matrix to be known beforehand. By an iterative procedure, involving the evaluation of determinants, the lower bound is increased andor the upper decreased until agreement is achieved between them to a specified number of digits. Multiple eigenvalues can not be determined by this method. All eigenvalues are obtained to the same number of significant figures, which should be especially helpful when working with a matrix whose eigenvalues have very wide dispersion. A discussion of scaling is included which is applicable to many matrix problems, regardless of the method used to get numerical results. A table appears which compares the results obtained from using this method with those of another, when both procedures were applied to a specific problem. A Fortran IV computer program has been written embodying the principles contained herein. Author
- Theoretical Mathematics