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A New and Efficient Program for Finding All Polynomial Roots

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dc.contributor.author Lang, Markus
Frenzel, Bernhard-Christian
dc.creator Lang, Markus
Frenzel, Bernhard-Christian
dc.date.accessioned 2007-10-31T00:50:51Z
dc.date.available 2007-10-31T00:50:51Z
dc.date.issued 1993-01-15
dc.date.submitted 2004-11-08
dc.identifier.uri http://hdl.handle.net/1911/20043
dc.description Tech Report
dc.description.abstract Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a new program which is a combination of Muller's and Newton's method. We use the former for computing a root of the deflated polynomial which is a good estimate for the root of the original polynomial. This estimate is improved by applying Newton's method to the original polynomial. Test polynomials up to the degree 10000 show the superiority of our program over the best methods to our knowledge regarding speed and accuracy, i.e., Jenkins/Traub program and the eigenvalue method. Furthermore we give a simple approach to improve the accuracy for spectral factorization in the case there are double roots on the unit circle. Finally we briefly consider the inverse problem of root finding, i.e., computing the polynomial coefficients from the roots which may lead to surprisingly large numerical errors.
dc.language.iso eng
dc.subject polynomial roots
dc.subject.other General DSP
dc.title A New and Efficient Program for Finding All Polynomial Roots
dc.type Tech Report
dc.citation.bibtexName techreport
dc.citation.journalTitle Rice University ECE Technical Report
dc.date.modified 2004-11-10
dc.contributor.center Digital Signal Processing (http://dsp.rice.edu/)
dc.subject.keyword polynomial roots
dc.citation.issueNumber TR93-08
dc.type.dcmi Text
dc.identifier.citation M. Lang and B. Frenzel, "A New and Efficient Program for Finding All Polynomial Roots," Rice University ECE Technical Report, no. TR93-08, 1993.

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  • ECE Publications [1045 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.