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On the Field of Values of the Inverse of a Matrix

Zachlin, Paul Francis

Abstract Details

2007, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
This dissertation concerns the field of values of the inverse of a matrix. Techniques of approximation of this set are considered for large, sparse matrices, and applications are discussed. A new method is presented that is similar in computational cost to previous methods, but may yield better approximations in practice. Also, a new technique for finding eigenvalue inclusion regions is presented, developed from the relationship between the field of values of the inverse and the eigenvalue extraction technique known as harmonic Rayleigh-Ritz. By intersecting these eigenvalue inclusion regions, a new characterization of the spectrum of a matrix is obtained. The technique for generating these regions can be generalized by replacing the field of values with other eigenvalue inclusion sets, and this is demonstrated using the Geršgorin region of a matrix.
David Singer (Advisor)
70 p.

Recommended Citations

Citations

  • Zachlin, P. F. (2007). On the Field of Values of the Inverse of a Matrix [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690

    APA Style (7th edition)

  • Zachlin, Paul. On the Field of Values of the Inverse of a Matrix. 2007. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690.

    MLA Style (8th edition)

  • Zachlin, Paul. "On the Field of Values of the Inverse of a Matrix." Doctoral dissertation, Case Western Reserve University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690

    Chicago Manual of Style (17th edition)