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Algorithms for symmetrical polynomials
Proceedings of the third ACM symposium on Symbolic and algebraic computation - SYMSAC '76, 1976A special representation for symmetrical polynomials is introduced. Algorithms for the ring operations and for several versions of Gauss' method to express an arbitrary symmetrical polynomial by the elementary symmetrical functions are given and analyzed. Empirical observations show that the representation which is the most economical in terms of space
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A polynomial algorithm for partitioning problems
ACM Transactions on Embedded Computing Systems, 2010This article takes a theoretical approach to focus on the algorithmic properties of hardware/software partitioning. It proposes a method with polynomial complexity to find the global optimum of an NP-hard model partitioning problem for 75% of occurrences under some practical conditions.
Seyed-Abdoreza Tahaee +1 more
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A Convergent Algorithm for Solving Polynomial Algorithms
Journal of the ACM, 1967The method of steepest descent is applied in a convergent procedure to determine the zeros of polynomials having either real or complex coefficients. By expressing the polynomials in terms of the Siljak functions, the methods are readily programmed on a digital computer.
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New Algorithms for Polynomial Multiplication
SIAM Journal on Computing, 1979Exploiting the structure of the 2-dimensional sorting problem associated with the polynomial product has been the strategy in the design of certain algorithms which are faster for a large class of problems than those found in the literature. First a parallel is drawn between GEN–MULT and Horowitz’s SORT–MULT algorithm [A sorting algorithm for ...
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An algorithm on quasi-ordinary polynomials
1989Let K be a field of characteristic O, and let R denote K[X] or K[[X]]. It is well known that the roots of a polynomial FisinR[Z] are fractional powers series in K[[X 1d/]], where Kmacr is a finite extension of K and disin N, and they can be obtained by applying the Newton Puiseux algorithm.
Maria Emilia Alonso +2 more
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A polynomial-based division algorithm
2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2003A polynomial-based division algorithm and a corresponding hardware structure are proposed. The proposed algorithm is shown to be competitive to other conventional algorithms like the Newton-Raphson algorithm for up to about 32 bits accuracy. For example, using Newton-Raphson with less than 12 bits accuracy of the initial approximation, requires 33 ...
Robert Hägglund +2 more
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Polynomial algorithms for projection and matching
1993The main purpose of this paper is to develop polynomial algorithms for the projection and matching operations on conceptual graphs. Since all interesting problems related to these operations are at least NP-complete — we will consider here the exhibition of a solution and counting the solutions — we propose to explore polynomial cases by restricting ...
Marie-Laure Mugnier, Michel Chein
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Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design, 1988The aim of this paper is to investigate the aspects of the formulation of geometric modeling algorithms in the Bernstein polynomial basis. Bernstein forms for various basic polynomial procedures required in such algorithms are developed and are found to be of similar complexity to their customary power forms.
Rida T. Farouki, V. T. Rajan
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Algorithms for adaptive factorization of polynomials
Signal Processing, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Probabilistic algorithms for sparse polynomials
1979In this paper we have tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins. These techniques can be used for an extremely wide class of problems and can applied to a number of different algorithms including Hensel's lemma.
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