Algebra of Polynomials in Several Variables for a Digital Computer
Journal of the ACM (JACM)
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Algorithm 224: Evaluation of determinant
Communications of the ACM
Algorithm 269: determinant evaluation [F3]
Communications of the ACM
PM, a system for polynomial manipulation
Communications of the ACM
Solutions of systems of polynomial equations by elimination
Communications of the ACM
Algorithms 41: Evaluation of determinant
Communications of the ACM
Algorithm 170: reduction of a matrix containing polynomial elements
Communications of the ACM
Communications of the ACM
LISP 1.5 Programmer's Manual
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On the subresultant PRS algorithm
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On algorithms for solving systems of polynomial equations
ACM SIGSAM Bulletin
Computing floating-point gröbner bases stably
Proceedings of the 2007 international workshop on Symbolic-numeric computation
IEEE Transactions on Computers
| Hi-index | 48.22 |
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.