A New and Efficient Program for Finding All Polynomial Roots

dc.citation.bibtexNametechreporten_US
dc.citation.issueNumberTR93-08en_US
dc.citation.journalTitleRice University ECE Technical Reporten_US
dc.contributor.authorLang, Markusen_US
dc.contributor.authorFrenzel, Bernhard-Christianen_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T00:50:51Zen_US
dc.date.available2007-10-31T00:50:51Zen_US
dc.date.issued1993-01-15en_US
dc.date.modified2004-11-10en_US
dc.date.submitted2004-11-08en_US
dc.descriptionTech Reporten_US
dc.description.abstractFinding 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.en_US
dc.identifier.citationM. Lang and B. Frenzel, "A New and Efficient Program for Finding All Polynomial Roots," <i>Rice University ECE Technical Report,</i> no. TR93-08, 1993.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20043en_US
dc.language.isoengen_US
dc.subjectpolynomial rootsen_US
dc.subject.keywordpolynomial rootsen_US
dc.subject.otherGeneral DSPen_US
dc.titleA New and Efficient Program for Finding All Polynomial Rootsen_US
dc.typeReporten_US
dc.type.dcmiTexten_US
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