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Tang, Tunan 04-21-2016.pdf (348.61 KB)
ETD Abstract Container
Abstract Header
Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications
Author Info
Tang, Tunan
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903
Abstract Details
Year and Degree
2016, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
This dissertation describes several new quadrature rules for the approximation of integrals determined by measures with support on the real axis or in the complex plane. Standard n-point Gauss rules are associated with symmetric tridiagonal matrices of order n. Averaged Gauss quadrature rules are obtained by 'flipping'; these tridiagonal matrices to obtain a quadrature rule of about twice the size. These averaged rules have been proposed by Spalevic. Gauss-type quadrature rules also can be defined when the measure has its support in the complex plane. These rules are associated with nonsymmetric tridiagonal matrices. This dissertation presents averaged Gauss-type quadrature rules associated with these Gauss-type quadrature rules. Also block extensions are described. These correspond to matrix-valued measures. Finally, averaged Szego quadrature rules are described. They extend standard Szego quadrature rules for the integration of function on the unit circle in the complex plane.
Committee
Lothar Reichel, Ph.D. (Advisor)
Jing Li, Ph.D. (Committee Member)
Xiaoyu Zheng, Ph.D. (Committee Member)
Arden Ruttan, Ph.D. (Committee Member)
Arvind Bansal, Ph.D. (Committee Member)
Subject Headings
Mathematics
Keywords
quadrature
;
numerical analysis
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Citations
Tang, T. (2016).
Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903
APA Style (7th edition)
Tang, Tunan.
Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications.
2016. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903.
MLA Style (8th edition)
Tang, Tunan. "Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications." Doctoral dissertation, Kent State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903
Chicago Manual of Style (17th edition)
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Document number:
kent1460403903
Download Count:
423
Copyright Info
© 2016, some rights reserved.
Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications by Tunan Tang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Kent State University and OhioLINK.