Show simple item record

dc.contributor.authorGragg, William B.
dc.date1993
dc.date.accessioned2016-07-27T17:22:15Z
dc.date.available2016-07-27T17:22:15Z
dc.date.issued1993
dc.identifier.citationGragg, William B. "Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle." Journal of Computational and Applied Mathematics 46.1 (1993): 183-198.en_US
dc.identifier.urihttp://hdl.handle.net/10945/49289
dc.description.abstractWe 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.en_US
dc.description.sponsorshipNational Science Foundationen_US
dc.format.extent16 p.en_US
dc.publisherElsevier Science Publishers B.V.en_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titlePositive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circleen_US
dc.typeArticleen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)en_US
dc.contributor.departmentApplied Mathematicsen_US
dc.subject.authorToeplitz matricesen_US
dc.subject.authorunitary Hessenberg matricesen_US
dc.subject.authorSzegő polynomialsen_US
dc.description.funderNational Science Foundationen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record