Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
Gragg, William B.
MetadataShow full item record
We show that the well-known Levinson algorithm for computing the inverse Cholesky factorization of positive definite Toeplitz matrices can be viewed as a special case of a more general process. The latter process provides a very efficient implementation of the Arnoldi process when the underlying operator is isometric. This is analogous with the case of Hermitian operators where the Hessenberg matrix becomes tridiagonal and results in the Hermitian Lanczos process. We investigate the structure of the Hessenberg matrices in the isometric case and show that simple modifications of them move all their eigenvalues to the unit circle. These eigenvalues are then interpreted as abscissas for analogs of Gaussian quadrature, now on the unit circle instead of the real line. The trapezoidal rule appears as the analog of the Gauss-Legendre formula.
Showing items related by title, author, creator and subject.
Toward joint Medical Logistics 2010 and beyond: process innovation and redesign of Class VIII supply chain at a medical logistics company Augustitus, Mary A.; Stevenson, Sonja L. (Monterey, California. Naval Postgraduate School, 2000-12);The purpose of this thesis is to evaluate current Class VIII supply chain procedures at a U.S. Medical Logistics Company (Med Log Co), process map the "as is" baseline process and propose possible "to be" process redesign ...
Stone, Adam H. (Monterey, California: Naval Postgraduate School, 2014-09);The application of systems engineering methodologies to the creative process provides opportunities to improve the creative capabilities of individuals and organizations. Through creativity and systems engineering research, ...
Damore, Kathryn M.; Damore, Paul C.; Swing, Kenneth (Monterey, CA; Naval Postgraduate School, 2018-06);The purpose of this project is to determine whether the current policy dictating the officer mess bill collection process on ships is efficient and cost effective, or whether the policy requires modification to reduce costs ...