Results 251 to 260 of about 75,717 (294)

The unified Taylor-Ito expansion

Journal of Mathematical Sciences, 2000
The authors transpose the known Taylor-Itô expansion for solutions of stochastic differential equations to the form which contains a smaller number of applied repeated stochastic integrals.
Kul'chitskij, O. Yu., Kuznetsov, D. F.
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Taylor Expansions of Distributions

Numerical Functional Analysis and Optimization, 2000
In (1.18) we uglified the classical Taylor expansion of holomorphic functions in a domain Ω in the complex plane \( \mathbb{C} \) , which in our context will be better denoted as \( {\mathbb{R}^2} \). But it provided an understanding of what can be expected when asking for Taylor expansions of (complex-valued) functions and distributions in \( {\mathbb{
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Taylor’s Expansion

1989
It was a great triumph in the early years of Calculus when Newton and others discovered that many known functions could be expressed as “polynomials of infinite order” or “power series,” with coefficients formed by elegant transparent laws. The geometrical series for 1/(1 − x) or 1/(1 + x2) $$\frac{1}{{1\; - \;x}} = 1 + x + {x^2} \cdots + {x^n ...
Richard Courant, Fritz John
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Taylor expansions for distributions

Mathematical Methods in the Applied Sciences, 1993
AbstractWe present the Taylor asymptotic expansion of a perturbed distribution of the form equation image is a smooth function defined in ℝn. First we present the one‐dimensional theory to illustrate the underlying concepts and then we discuss the multi‐dimensional case. We find that various known results follow as special limits of our results.
Estrada, R., Kanwal, R. P.
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Optical flow and the Taylor expansion

Pattern Recognition Letters, 1986
Abstract An algorithm is proposed for computing the direction of translational motion of a moving rigid body from the resulting optical flow field. It requires the coefficients of a Taylor expansion of the flow field to second order. An explicit connection is made between this algorithm and one due to Longuet-Higgins that applies when the body ...
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Stochastic Taylor Expansions

1992
In this chapter stochastic Taylor expansions are derived and investigated. They generalize the deterministic Taylor formula as well as the Ito formula and allow various kinds of higher order approximations of functionals of diffusion processes to be made.
Peter E. Kloeden, Eckhard Platen
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Taylor expansions and applications

2015
The Taylor expansion of a function around a real point x 0 is the representation of the map as sum of a polynomial of a certain degree and an infinitesimal function of order bigger than the degree. It provides an extremely effective tool both from the qualitative and the quantitative point of view.
Claudio Canuto, Anita Tabacco
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Matrix Calculus Operations and Taylor Expansions

SIAM Review, 1973
In problems of large dimensional complexities, matrix methods are frequently the favored mathematical tools. In this paper some extensions of matrix methods to calculus operations are introduced. Consistent array structural definitions are given for derivatives of matrix-valued functions with respect to matrices, for matrix differentials, and for ...
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Approximation of the derivatives beyond Taylor expansion

Computers & Mathematics with Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiuyan Xu, Zhiyong Liu 0004
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Taylor Expansion

2021
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