Results 11 to 20 of about 40,126 (265)
Classical and Quantum Algorithms for Tensor Principal Component Analysis [PDF]
Quantum, 2020 We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a $quartic$ speedup while using exponentially smaller space than the fastest classical spectral ...
Matthew B. Hastings
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Decomposition Algorithms for Tensors and Polynomials
SIAM Journal on Applied Algebra and Geometry, 2023 Abstract. We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present new methods to compute the decomposition of a general plane quintic in seven powers, and of a general space cubic ...
Antonio Laface +2 more
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Compensated Evaluation of Tensor Product Surfaces in CAGD
Mathematics, 2020 In computer-aided geometric design, a polynomial surface is usually represented in Bézier form. The usual form of evaluating such a surface is by using an extension of the de Casteljau algorithm. Using error-free transformations, a compensated version of
Jorge Delgado Gracia
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Algorithms for trigonometric polynomials [PDF]
Proceedings of the 2001 international symposium on Symbolic and algebraic computation, 2001 In this paper we present algorithms for simplifying ratios of trigonometric polynomials and algorithms for dividing, factoring and computing greatest common divisors of trigonometric polynomials, that is, polynomials in sin(x) and cos(x).
Jamie Mulholland, Michael B. Monagan
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Simple Algorithm for GCD of Polynomials
WSEAS TRANSACTIONS ON MATHEMATICS, 2022 Based on the Bezout approach we propose a simple algorithm to determine the gcd of two polynomials which doesn’t need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only n steps for polynomials of degree n.
Pasquale Nardone, Giorgio Sonnino
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A Polynomial Quantum Algorithm for Approximating the Jones Polynomial [PDF]
Algorithmica, 2006 The Jones polynomial, discovered in 1984, is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten) to be intimately connected to Topological Quantum Field Theory (TQFT).
Dorit Aharonov +2 more
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Deterministic Algorithms for Solving Boolean Polynomial Equations Based on Channel Coding Theory
IEEE Access, 2020 Solving the satisfiability problems of Boolean polynomial equations is still an open challenge in the fields of mathematics and computer science.
Guangfu Wu +5 more
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Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018 The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general.
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Algorithms For Positive Polynomial Approximation [PDF]
SIAM Journal on Numerical Analysis, 2019 We propose several algorithms for positive polynomial approximation. The main tool is a novel iterative method to compute nonnegative interpolation polynomials at any order, which is shown to converge under conditions that make it suitable for the numerical approximation of positive functions.
Charles, Frédérique +2 more
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An Algorithm for Polynomial Operations [PDF]
The Computer Journal, 1967 Recent interest in the mechanization of operations in polynomial algebra has led to the production of programs such as ALPAK, FORMAC, Formula ALGOL (with associated translator), GRAD Assistant and PM. (See the survey in Comm. ACM, Vol. 9, No. 8, August 1966; and Brown, Hyde and Tague, 1962-3, Williams, 1962, and Collins, 1966a.) These programs provide ...
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