Concurrent Computing: Numerical Algorithms and Some Applications.
Annual rept. 15 Jul 85-14 Jul 86,
MASSACHUSETTS INST OF TECH CAMBRIDGE
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An important issue in harmonic retrieval problems, as in most computational problems, is the well-posedness of a particular problem instance. Specifically, when is a harmonic signal reconstruction by these methods particularly densitive to additive noise A definitive answer to this question was obtained in the form of a condition number for harmonic retrieval problems and is based on the Vandermonde determinant of the harmonic frequencies. This result was obtained via a combination of relationships using classical trigonometric moment theory and Toeplitz matrix conditioning. A fundamental new result, due to Davis and Bhatia, on the spectral sensitivity of unitary matrices was used. The result first appeared in the Princeton Conference on Information Systems and Sciences Proceedings in a paper titled Conditioning of Eigenvector Methods for Beamforming Problems while more recently a survey of this work will form the basis for an invited presentation at the upcoming IEEE Workshop on Spectrum Estimation. That survey is titled The Sensitivity of Beamforming Problems.