Results 11 to 20 of about 31,275 (174)
An Extended Kalman Filter with Remainder Terms and Correlation Compensation for Nonlinear State Monitoring and Soft Sensing [PDF]
SensorsIn networked sensing systems, nonlinear state monitoring and soft sensing are widely used to reconstruct key variables that cannot be directly measured in real time. For such nonlinear estimation tasks, the Extended Kalman Filter (EKF) is a commonly used
Jinhao Ke, Chenglin Wen
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Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder [PDF]
Journal of Applied Mathematics, 2014 The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function.
Isaac Fried
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, 2017 Summary: In this note we derive a new Taylor remainder, which extends the well known Lagrange remainder as well as the obscure Gonçalves remainder.
Persson, Lars-Erik, Rafeiro, Humberto
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Historical synopsis of the Taylor remainder
, 2017 In this paper we give an historical synopsis of various Taylor remainders and theirdierent proofs (without being exhaustive). We overview the formulas and the proofs given bysuch names as Bernoulli, Taylor, MacLaurin, Lagrange, Lacroix, Cauchy, Schlomilch, Roche,Cox, Turquan, Bourget, Koenig, Darboux, Amigues, Teixeira, Peano, Blumenthal, Wolfe ...
Persson, Lars-Erik +2 more
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Automatically Bounding the Taylor Remainder Series: Tighter Bounds and New Applications
CoRR, 2022 We present a new algorithm for automatically bounding the Taylor remainder series. In the special case of a scalar function $f: \mathbb{R} \to \mathbb{R}$, our algorithm takes as input a reference point $x_0$, trust region $[a, b]$, and integer $k \ge 1$, and returns an interval $I$ such that $f(x) - \sum_{i=0}^{k-1} \frac {1} {i!} f^{(i)}(x_0) (x ...
Matthew Streeter, Joshua V. Dillon
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Taylor's Expansion Revisited: A General Formula for the Remainder [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We give a new approach to Taylor's remainder formula, via a generalization of Cauchy's generalized mean value theorem, which allows us to include the well-known Schölomilch, Lebesgue, Cauchy, and the Euler classic types, as particular cases.
José Juan Rodríguez Cano +1 more
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Fractal and Fractional, 2022 A nonlinear fractional differential equation with a Caputo derivative of order α is studied. This problem is discretized by using the L1 scheme on an arbitrary nonuniform mesh.
Tao Yang +3 more
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Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus
Journal of Mathematics, 2021 The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus.
Francisco Martínez +3 more
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Extrapolation of Duffing Equation Solution by Using RBF Network
Современные информационные технологии и IT-образование, 2021 The article considers the problem of approximation of the solution of the Cauchy problem for an ordinary differential equation of the second order. The approximation scheme is based on the Taylor expansion of the solution with a remainder in the Lagrange
Tatyana Lazovskaya +3 more
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Explicit Construction of the Inverse of an Analytic Real Function: Some Applications
Mathematics, 2020 In this paper, we introduce a general procedure to construct the Taylor series development of the inverse of an analytical function; in other words, given y=f(x), we provide the power series that defines its inverse x=hf(y). We apply the obtained results
Joaquín Moreno +2 more
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