Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-16T03:36:54.904Z Has data issue: false hasContentIssue false
  • English
  • Français

XXIII.—Studies in Practical Mathematics. VII. On the Theory of Methods of Factorizing Polynomials by Iterated Division*

Published online by Cambridge University Press:  14 February 2012

A. C. Aitken
A. C. Aitken
Affiliation:
Mathematical Institute, University of Edinburgh.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The division of one polynomial by another is studied with the object of ascertaining the errors produced in the coefficients of successive remainders by small errors in the coefficients of the divisor. It is shown that the matrix which effects this transformation of errors is a polynomial in the rational canonical matrix for which the divisor polynomial is characteristic. The theory gives rise to a numerous class of iterative processes for finding an exact factor, such as the extant method based on the penultimate remainder, Bairstow's iterative method of finding a quadratic factor, and many others. Some new suggestions are made for accelerating convergence.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 4 , 1952 , pp. 326 - 335
Copyright
Copyright © Royal Society of Edinburgh 1952

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES TO LITERATURE

Aitken, A. C., 1950. Proc. Roy. Soc. Edin., A, LXIII, 174–191.Google Scholar
Bairstow, L., 1920. Applied Aerodynamics, Longmans, Green & Co., London.Google Scholar
Friedman, B., 1949. Commun. Pure Appi. Math., II, 195–208.Google Scholar
Fry, T. C., 1945. Quart. Appi. Math., III, 89–105.Google Scholar
Lin, S. N., 1939. Thesis for Sc.D., Massachusetts Institute of Technology.Google Scholar
Lin, S. N., 1941. Journ. Math. Phys., xx, 231–241.Google Scholar
Lin, S. N., 1943. Journ. Math. Phys., xxi, 60–77.Google Scholar
Luke, Y. L., and Ufford, D., 1951. Journ. Math. Phys., xxx, 95–109.Google Scholar
Sealy, E. H., 1940. Thesis for Ph.D., University of Edinburgh.Google Scholar
Whittaker, E. T., and Robinson, G., 1944. The Calculus of Observations, 4th ed., Blackie & Sons, London and Glasgow.Google Scholar