H. A. Luther – Communications of the ACM

Research and Advances Mar 1 1964

A class of iterative techniques for the factorization of polynomials

A method of iteration is developed in terms of a function of somewhat arbitrary character. Sufficient conditions are given for convergence of the process, yielding factors of arbitrary degree for polynomials in one variable. Both Lin's method and Newton's method occur as special cases.

Theory

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Research and Advances Mar 1 1963

An interative factorization techniques for polynomials

An iterative technique is displayed whereby factors of arbitrary degree can be found for polynomials in one variable. Convergence is shown to occur always if a certain Jacobian does not vanish and if the initial approximation to a factor is near enough to an actual factor. The process is simply programmed, and preliminary results indicate it to be well adapted to use with digital computers. For factors of degree two, the technique is similar to that of Bairstow, the present method being somewhat simpler.

Research and Advances Aug 1 1962

A finite sequentially compact process for the adjoints of matrices over arbitrary integral domains

Research and Advances Aug 1 1961

A note on multiple precision arithmetic

Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed “radix t”, that is, in the form a = a0 + a1t + ··· + antn where ai are of like sign and have magnitudes less than t. t is a positive integer determined by the word length of the computer. Consider the expression c = a ± b = (a0 ± b0) + (a1 ± b1)t + ··· + (an ± bn)tn. Here ai ± bi may exceed the storage capacity of one word or may have a sign different from c.

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