Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Kelly, A. Newell (1965)
Information processing language-V manualMathematics of Computation, 19
(1962)
COMIT Programmers Reference Manual
G. Collins (1966)
PM, a system for polynomial manipulationCommun. ACM, 9
D. Digby (1963)
Algorithm 159: determinantCommunications of the ACM, 6
(1965)
Determinant evaluation (Algorithm 269)
Paul Hennion (1963)
Algorithm 170: reduction of a matrix containing polynomial elementsCommun. ACM, 6
Josef Solomon (1961)
Algorithms 41: Evaluation of determinantCommunications of the ACM, 4
J. Moses (1966)
Solutions of systems of polynomial equations by eliminationCommun. ACM, 9
(1961)
Evaluation of determinant (Algorithm 41)
G. Collins (1967)
Subresultants and Reduced Polynomial Remainder SequencesJ. ACM, 14
(1966)
Multiple solution sets for non-linear mechanics problems
W. Brown, J. Hyde, B. Tague (1963)
The alpak system for nonnumerical algebra on a digital computer
K. Priebe (1964)
Certification of Algorithm 170: Reduction of a Matrix Containing Polynomial ElementsCommunications of the ACM, 7
(1960)
Comput. Center and Res. Lab. of Electronics, MIT
(1964)
Non-linear matrix algebra and engineering applications
(1966)
A method of solving sets of non-linear algebraic equations
J. Weizenbaum (1963)
Symmetric list processorCommun. ACM, 6
(1950)
Modern Algebra, Vols. 1 and 2
Arthur Panton, W. Burnside
Theory of equations
Leo Rotenberg (1964)
Algorithm 224: Evaluation of determinantCommun. ACM, 7
L. Williams (1962)
Algebra of Polynomials in Several Variables for a Digital ComputerJ. ACM, 9
M. Bôcher (2013)
Introduction to higher algebra
J. Pfann, J. Straka (1965)
Algorithm 269: determinant evaluation [F3]Commun. ACM, 8
G. Collins (1966)
Polynomial Remainder Sequences and DeterminantsAmerican Mathematical Monthly, 73
K. Hirsch, C. Macduffee (1954)
Theory of EquationsThe Mathematical Gazette, 39
(1964)
USPENSKY, J. -V. T h e o r y o f E q u a t i o n s
(1963)
Comm. ACM
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.
Communications of the ACM – Association for Computing Machinery
Published: Jan 1, 1969
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.