Computing Popov Forms of Polynomial Matrices

Computing Popov Forms of Polynomial Matrices

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This thesis gives a deterministic algorithm to transform a row reduced matrix to canon- ical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimensi...

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Main Author: Sarkar, Soumojit
Language:en
Published: 2012
Subjects:
Computer Science
Online Access:http://hdl.handle.net/10012/6472
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OWTU.10012-64722013-10-04T04:11:22ZSarkar, Soumojit2012-01-19T18:13:17Z2012-01-19T18:13:17Z2012-01-19T18:13:17Z2012-01-12http://hdl.handle.net/10012/6472This thesis gives a deterministic algorithm to transform a row reduced matrix to canon- ical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimension and degree as R. Randomization can be used to extend the algorithm for rectangular input matrices of full row rank. Thus we give a Las Vegas algorithm that computes the Popov decomposition of matrices of full row rank. We also show that the problem of transforming a row reduced matrix to Popov form is at least as hard as polynomial matrix multiplication.enComputing Popov Forms of Polynomial MatricesThesis or DissertationSchool of Computer ScienceMaster of MathematicsComputer Science
collection NDLTD
language en
sources NDLTD
topic Computer Science
spellingShingle Computer Science
Sarkar, Soumojit
Computing Popov Forms of Polynomial Matrices
description This thesis gives a deterministic algorithm to transform a row reduced matrix to canon- ical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimension and degree as R. Randomization can be used to extend the algorithm for rectangular input matrices of full row rank. Thus we give a Las Vegas algorithm that computes the Popov decomposition of matrices of full row rank. We also show that the problem of transforming a row reduced matrix to Popov form is at least as hard as polynomial matrix multiplication.
author Sarkar, Soumojit
author_facet Sarkar, Soumojit
author_sort Sarkar, Soumojit
title Computing Popov Forms of Polynomial Matrices
title_short Computing Popov Forms of Polynomial Matrices
title_full Computing Popov Forms of Polynomial Matrices
title_fullStr Computing Popov Forms of Polynomial Matrices
title_full_unstemmed Computing Popov Forms of Polynomial Matrices
title_sort computing popov forms of polynomial matrices
publishDate 2012
url http://hdl.handle.net/10012/6472
work_keys_str_mv AT sarkarsoumojit computingpopovformsofpolynomialmatrices
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