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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.
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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

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References

REFERENCES TO LITERATURE

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