dc.contributor.author Cheng, Howard en dc.date.accessioned 2006-08-22 14:27:17 (GMT) dc.date.available 2006-08-22 14:27:17 (GMT) dc.date.issued 2003 en dc.date.submitted 2003 en dc.identifier.uri http://hdl.handle.net/10012/1088 dc.description.abstract In this thesis we study algorithms for computing normal forms for matrices of Ore polynomials while controlling coefficient growth. By formulating row reduction as a linear algebra problem, we obtain a fraction-free algorithm for row reduction for matrices of Ore polynomials. The algorithm allows us to compute the rank and a basis of the left nullspace of the input matrix. When the input is restricted to matrices of shift polynomials and ordinary polynomials, we obtain fraction-free algorithms for computing row-reduced forms and weak Popov forms. These algorithms can be used to compute a greatest common right divisor and a least common left multiple of such matrices. Our fraction-free row reduction algorithm can be viewed as a generalization of subresultant algorithms. The linear algebra formulation allows us to obtain bounds on the size of the intermediate results and to analyze the complexity of our algorithms. We then make use of the fraction-free algorithm as a basis to formulate modular algorithms for computing a row-reduced form, a weak Popov form, and the Popov form of a polynomial matrix. By examining the linear algebra formulation, we develop criteria for detecting unlucky homomorphisms and determining the number of homomorphic images required. en dc.format application/pdf en dc.format.extent 586044 bytes dc.format.mimetype application/pdf dc.language.iso en en dc.publisher University of Waterloo en dc.rights Copyright: 2003, Cheng, Howard. All rights reserved. en dc.subject Computer Science en dc.subject computer algebra en dc.subject normal form en dc.subject polynomial matrix en dc.title Algorithms for Normal Forms for Matrices of Polynomials and Ore Polynomials en dc.type Doctoral Thesis en dc.pending false en uws-etd.degree.department School of Computer Science en uws-etd.degree Doctor of Philosophy en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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