Sign In

Communications of the ACM

Communications of the ACM

Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm

Algorithms for computing the resultant of two polynomials in several variables, a key repetitive step of computation in solving systems of polynomial equations by elimination, are studied. Determining the best algorithm for computer implementation depends upon the extent to which extraneous factors are introduced, the extent of propagation of errors caused by truncation of real coeffcients, memory requirements, and computing speed. Preliminary considerations narrow the choice of the best algorithm to Bezout's determinant and Collins' reduced polynomial remainder sequence (p.r.s.) algorithm. Detailed tests performed on sample problems conclusively show that Bezout's determinant is superior in all respects except for univariate polynomials, in which case Collins' reduced p.r.s. algorithm is somewhat faster. In particular Bezout's determinant proves to be strikingly superior in numerical accuracy, displaying excellent stability with regard to round-off errors. Results of tests are reported in detail.

The full text of this article is premium content


No entries found

Log in to Read the Full Article

Sign In

Sign in using your ACM Web Account username and password to access premium content if you are an ACM member, Communications subscriber or Digital Library subscriber.

Need Access?

Please select one of the options below for access to premium content and features.

Create a Web Account

If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.

Join the ACM

Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.

Subscribe to Communications of the ACM Magazine

Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.

Purchase the Article

Non-members can purchase this article or a copy of the magazine in which it appears.
Sign In for Full Access
» Forgot Password? » Create an ACM Web Account