General polynomial roots and their multiplicities in O(N)memory and O(N 2)Time

For a given real or complex polynomial p of degree n we modify the Euclidean algorithm to find a general tridiagonal matrix representation T of the monic version of p and then use the tridiagonal DQR eigenvalue algorithm on T in order to find all roots ofp with their multiplicities in O(n 2 ) operat...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 46; no. 4; pp. 327 - 359
Main Author Uhlig, Frank
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.10.1999
Subjects
AMS Subject Classifications: I2DI0. 65H05. 65F15. 65F50. 65Y20. 15A18. 15A57. 11C99. 12-04
complexity
DQR algorithm
eigenvalue
Euclidean algorithm
operations count
Polynomial root
root multiplicity
tridiagonal matrix
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ISSN0308-1087
1563-5139
DOI10.1080/03081089908818625

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Summary:For a given real or complex polynomial p of degree n we modify the Euclidean algorithm to find a general tridiagonal matrix representation T of the monic version of p and then use the tridiagonal DQR eigenvalue algorithm on T in order to find all roots ofp with their multiplicities in O(n 2 ) operations and 0(n) storage. We include details of the implementation and comparisons with several, standard and recent, essentially 0(n 3 ) polynomial root finders.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081089908818625