Simple, Effective Computation of Principal Eigen-Vectors and Their Eigenvalues and Application to High-Resolution Estimation of Frequencies
Final rept. Oct 84-Oct 85,
RHODE ISLAND UNIV KINGSTON DEPT OF ELECTRICAL ENGINEERING
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We present the results of an investigation of the Prony-Lanczos method and the power method for simple computation of approximations to a few eigenvectors and eigenvalues of a Hermitian matrix. We are motivated by realization of high resolution signal processing in an integrated circuit. The computational speeds of the above methods are analyzed. They are completely dependent on the speed of a matrix vector product operation. If only a few eigenvalues or eigenvectors are needed, the suggested methods can substitute for the slower methods of the LINPACK or EISPACK subroutine libraries. The accuracies of the suggested methods are evaluated using matrices formed from simulated data consisting of two sinusoids plus gaussian noise. Comparisons are made with the corresponding eigenvalues and eigenvectors obtained using LINPACK. Also the accuracies of frequency estimates obtained from the eigenvectors are compared.
- Electrical and Electronic Equipment
- Theoretical Mathematics