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Multiple zeros of polynomialsFor polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.
Document ID
19740023929
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Wood, C. A. (Oklahoma State Univ. Stillwater, OK, United States)
Date Acquired
September 3, 2013
Publication Date
January 1, 1974
Subject Category
Mathematics
Report/Patent Number
NASA-CR-139675
Accession Number
74N32042
Funding Number(s)
CONTRACT_GRANT: NGR-37-002-084
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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