A local construction of the Smith normal form of a matrix polynomial

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We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular operations to the original matrix row by row (or column by column). The performance of the algorithm in exact arithmetic is reported for several test cases.

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Wilkening, Jon & Yu, Jia September 1, 2008.

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We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular operations to the original matrix row by row (or column by column). The performance of the algorithm in exact arithmetic is reported for several test cases.

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  • Journal Name: Journal of Symbolic Computation

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  • Report No.: LBNL-1294E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 944574
  • Archival Resource Key: ark:/67531/metadc893943

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  • September 1, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:18 p.m.

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Wilkening, Jon & Yu, Jia. A local construction of the Smith normal form of a matrix polynomial, article, September 1, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc893943/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.