Dennis C. Smolarski, S.J.'s Personal Information Page

Curriculum Vitæ

DENNIS C. SMOLARSKI, S.J.

Born: September 2, 1947, Harvey, Illinois

Mailing Address:

Rev. Dennis C. Smolarski, S.J.
Jesuit Community
Santa Clara University
500 El Camino Real
Santa Clara, CA 95053-1600
Work Address:
Rev. Dennis C. Smolarski, S.J.
Department of Mathematics and Computer Science
Santa Clara University
500 El Camino Real
Santa Clara, CA 95053-0290
Office (Math/CS Department) Phone Number: 408 - 554-4174
Math/CS Department Phone Number: 408 - 554-4525
Math/CS Department FAX Number: 408 - 554-2370
Jesuit Community Phone Number: 408 - 554-4124
Jesuit Community FAX Number: 408 - 554-4795
E-mail Address: dsmolarski@scu.edu
Homepage URL:
https://webpages.scu.edu/ftp/dsmolarski

(Publication links:

Also given below. )

Education:

Doctoral Areas of Specialization (University of Illinois) Dissertation Abstract

In 1975, T. A. Manteuffel developed a method for the iterative solution of a non-symmetric linear system, Ax = b, when the eigenvalues have positive real parts. The iterative parameters are reciprocals of the roots of a scaled and translated Chebyshev polynomial and depend upon an ellipse enclosing the spectrum of the system matrix.

In some applications, a matrix will occur whose spectrum is not well approximated by an ellipse. In this thesis, a method is developed to determine optimal iteration parameters for use in a complex version of Richardson's iteration for a spectrum contained in any simply-connected bounded open set (in practice, a polygon symmetric with respect to the real axis).

The proposed method is a generalization of algorithms found in a 1958 paper of E. L. Stiefel in which real orthogonal polynomials were used. In this thesis, Stiefel's work is extended to complex orthogonal and bi-orthogonal polynomials. In addition, numerical methods are developed to obtain the desired iteration parameters by means of least squares theory. Results are presented which show that the methods of this thesis compare favorably to Manteuffel's method and the Lanczos algorithm for test matrices whose spectra had pre-determined shapes.

Employment

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Religious Biographical Synopsis

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My email address is dsmolarski "at" scu.edu

This information page last updated 8 April 2022.