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The Jenkins–Traub algorithm for polynomial zeros is a fast globally convergent iterative polynomial root-finding method published in 1970 by Michael A. Jenkins and Joseph F. Traub. They gave two variants, one for general polynomials with complex coefficients, commonly known as the "CPOLY" algorithm, and a more complicated variant for the ...
Finding the real roots of a polynomial with real coefficients is a problem that has received much attention since the beginning of 19th century, and is still an active domain of research. Most root-finding algorithms can find some real roots, but cannot certify having found all the roots.
Also deflation, i.e. removal of roots already found, is not needed and every test starts with the full-precision, original polynomial. And, remarkably, this polynomial has never to be evaluated. However, the smaller the disks become, the more the coefficients of the corresponding 'scaled' polynomials will differ in relative magnitude.
Urbain Le Verrier (1811–1877) The discoverer of Neptune.. In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial = of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier.
The Lindsey–Fox algorithm, named after Pat Lindsey and Jim Fox, is a numerical algorithm for finding the roots or zeros of a high-degree polynomial with real coefficients over the complex field. It is particularly designed for random coefficients but also works well on polynomials with coefficients from samples of speech, seismic signals, and ...
Every polynomial can be scaled in domain and range such that in the resulting polynomial the first and the last coefficient have size one. If the size of the inner coefficients is bounded by M , then the size of the inner coefficients after one stage of the Graeffe iteration is bounded by n M 2 {\displaystyle nM^{2}} .
Bairstow's approach is to use Newton's method to adjust the coefficients u and v in the quadratic + + until its roots are also roots of the polynomial being solved. The roots of the quadratic may then be determined, and the polynomial may be divided by the quadratic to eliminate those roots.
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]