Results 231 to 240 of about 5,753 (265)

Multivariate Polynomial Multiplication on GPU

Procedia Computer Science, 2016
AbstractMultivariate polynomial multiplication is a fundamental operation which is used in many scientific domains, for example in the optics code for particle accelerator design at CERN. We present a novel and efficient multivariate polynomial multiplication algorithm for GPUs using floating-point double precision coefficients implemented using the ...
Diana Andreea Popescu, Rogelio Tomas Garcia   +1 more
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Sparse multiplication for skew polynomials

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020
Consider the skew polynomial ring L[x; σ], where L is a field and σ is an automorphism of L of order r. We present two randomized algorithms for the multiplication of sparse skew polynomials in L[x;σ]. The first algorithm is Las Vegas; it relies on evaluation and interpolation on a normal basis, at successive powers of a normal element. For inputs A, B
Mark Giesbrecht, Qiao-Long Huang, Éric Schost   +2 more
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On Multiplication of Polynomials Modulo a Polynomial

SIAM Journal on Computing, 1980
The multiplicative complexity of the direct product of algebras $A_p $ of polynomials modulo a polynomial P is studied. In particular, we show that if P and Q are irreducible polynomials then the multiplicative complexity of $A_{\text{P}} \times A_{\text{Q}} $ is $2\deg ({\text{P}})\deg ({\text{Q}}) - {\text{k}}$, where k is the number of factors of P ...
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Bivariate polynomial multiplication

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), 2002
We study the multiplicative complexity and the rank of the multiplication in the local algebras R/sub m,n/=k[x,y]/(x/sup m+1/,y/sup n+1/) and T/sub n/=k[x,y]/(x/sup n+1/,x/sup n/y,...,y/sup n+1/) of bivariate polynomials. We obtain the lower bounds (21/3-0(1))/spl middot/dim R/sub m,n/, and (2 1/2 -0(1))/spl middot/dim T/sub n/ for the multiplicative ...
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New Algorithms for Polynomial Multiplication

SIAM Journal on Computing, 1979
Exploiting 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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Multiplication operator on a matrix polynomial

Ukrainian Mathematical Journal, 1992
Summary: It is shown, how the study of the perturbed multiplication operator by a matrix polynomial in the space \(L_ 2(\mathbb{R},\mathbb{C}^ n)\) can be reduced to the study of the perturbed multiplication operator by the independent variable in the space \(L_ 2(\mathbb{R},\omega,\mathbb{C}^ n)\) with weight \(\omega\), fulfilling the Muckenhoupt ...
Mikityuk, Ya. V., Al'-Tundzhi, M.
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Multiplication of a Schubert polynomial by a Schur polynomial

Annals of Combinatorics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Integer Polynomials with Multiple Roots

Mathematika, 2007
The authors prove the following result Theorem 1. Let \(P(X)\) be a polynomial of degree \(n \geq 2\). Denote by \(\alpha\) a zero of \(P\) of order \(s\) and \(\beta\) another zero of \(P\) of order \(t\geq s\), then \[ | \alpha-\beta| \geq 2^{-n/(2t)}(n+1)^{-n/(2s)-3n/(4st)}\text{H}(P)^{-n/(st)}\max\{1,| \alpha| \}\max\{1,| \beta| \}, \] where ...
Amou, Masaaki, Bugeaud, Yann
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An algorithm for the multiplication of symmetric polynomials

ACM Transactions on Mathematical Software, 1988
Although the cycle index polynomial for a permutation group can often be easily determined, expansion of the figure counting series in a Po´lya enumeration presents computational difficulties for object sets with higher degrees of symmetry and more than modest size.
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Bivariate polynomial multiplication patterns

1995
Motivated by multiplication of numerical univariate polynomials with various kinds of truncation we study corresponding bivariate problems A(x, y)·B(x, y) = C(x, y) in the algebraic setting with indeterminate coefficients over suitable ground fields, counting essential multiplications only.
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