Results 1 to 10 of about 2,367,547 (250)
Quantum computing of semiclassical formulas [PDF]
Physical Review E, 2008 We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from ...
Georgeot, Bertrand, Giraud, Olivier
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Efficient computation of the Zassenhaus formula [PDF]
Computer Physics Communications, 2012 A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing the minimum number of terms. The recursion can be easily implemented in a symbolic algebra package and requires much less computational ...
Fernando Casas +2 more
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Effective computations of the Atiyah-Bott formula [PDF]
Journal of Symbolic Computation, 2022 We present an implementation of the Atiyah-Bott residue formula for $\overline{M}_{0,m}(\mathbb{P}^{n},d)$. We use this implementation to compute a large number of Gromov-Witten invariants of genus $0$, including intersection numbers of rational curves on general complete intersections. We also compute some numbers of rational contact curves satisfying
Giosuè Muratore, Csaba Schneider
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, 2020 In this chapter, we will go one step beyond the Hello, World! example of the first chapter, and introduce programming with mathematical formulas. Such formulas are essential parts of most programs written for scientific applications, and they are also useful for introducing the concept of variables, which is a fundamental part of all programming ...
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Quadrature formula for computed tomography
Journal of Approximation Theory, 2010 The authors present a Gaussian quadrature formula for integrals of the form \[ \int_B f(x,y) U_n(x\cos\theta+y\sin\theta)\,dx\,dy \] over the unit disk \(B\) for the Chebyshev polynomials \(U_n\) of second kind. The formula involves \(n\) Radon projections on \(B\), has the maximal degree \(3n+1\) of precision, and is unique by this property. It may be
Bojanov, Borislav, Petrova, Guergana
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The formula-controlled logical computer “Stanislaus” [PDF]
Mathematics of Computation, 1960 The evaluation of a formula of propositional calculus is considerably simplified if this formula is written in the parenthesis-free notation of the Warsaw School, [1]. The Warsaw notation may be formulated in the following way: There are symbols for operations, e.g.: N for negation; K for conjunction; A for disjunction; E for equivalence; C for ...
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On computing Gauss-Kronrod quadrature formulae [PDF]
Mathematics of Computation, 1986 We discuss the use of Newton’s method for computing Gauss-Kronrod quadrature formulae from modified moments. The underlying nonlinear maps are analyzed from the point of view of numerical condition. A method is indicated of computing the polynomial whose zeros are the Kronrod nodes.
CALIO', FRANCA +2 more
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A formula for computation of the real stability radius [PDF]
Automatica, 1995 The authors present a method for approximation of the maximal perturbations of a real matrix. Its eigenvalues have to stay in a prescribed area in the complex plane. Such a measure of robustness of the eigenvalue clustering property is called a real stability radius.
Li Qiu 0001 +5 more
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Formulas for series computations [PDF]
Applicable Algebra in Engineering, Communication and Computing, 1992 Let \(K\) be a field of characteristic 0, \(\overline K\) an algebraic closure of \(K\) and \(K(x)\) the rational function field in one variable \(x\) over \(K\). The paper describes an algorithm that computes for an element \(f\) of \(K(x)\) for each \(n\in\mathbb N\) and \(m\in\{1,\dots,n\}\) a univariate polynomial \(B_{nm}\) over \(K\) whose roots ...
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Multilinear formulas and skepticism of quantum computing
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, 2004 Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural set of quantum states that can account for all experiments performed to date, but not for Shor's factoring algorithm.
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