“…PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. …”
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“…Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Intervals Central Difference Interpolation Formulae Inverse Interpolation Numerical Differentiation Numerical Integration Numerical Solution of Ordinary Differential Equations Solution of Linear Equations Curve Fitting Eigen Values and Eigen Vectors of a Matrix Regression Analysis…”
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“…The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.…”
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“…Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. …”
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“…It relies on the use of fast computers with a sophisticated mathematical computing language such as Mathematica to perform the required integration numerically so that the researcher can focus on the physics of the inductance calculation and not on the numerical integration.…”
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“…They can occur in Newton’s recursion and in numerical integration.…”
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“…Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi–Taupin equations and wavefront propagation. …”
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“…Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focused primarily on the theoretical aspects. …”
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“…Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. …”
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“…Moreover, the impact of different interpolation methods on the numerical integration process was observed. The idea for this thesis work started during an internship at CERN (European Organization for Nuclear Research, Geneva, Switzerland), from September 2017 to November 2018. …”
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“…Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. …”
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“…These are the straight-forward integration of the n- body problem, the statistical model description, the Monte Carlo technique, the Boltzmann moment approach. Direct numerical integration can now be applied to the dynamical evolution of star clusters containing up to 500 stars, which includes small to medium open stellar clusters, while statistical and Monte Carlo descriptions are better suited for systems of at least several thousand stars. …”
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“…This paper presents an adaptive control algorithm for realizing a vibratory angle measuring gyroscope so that rotation angle can be directly measured without integration of angular rate, thus eliminating the accumulation of numerical integration errors. The proposed control algorithm uses a trajectory following approach and the reference trajectory is generated by an ideal angle measuring gyroscope driven by the estimate of angular rate and the auxiliary sinusoidal input so that the persistent excitation condition is satisfied. …”
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“…In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. …”
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“…In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. …”
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“…A natural and convenient approach to constructing new expRK methods on the base of traditional RK methods is provided. In the numerical integration of the one-gene, two-gene, and p53-mdm2 regulatory systems, the new expRK methods are shown to be more accurate than their prototype RK methods. …”
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“…We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. …”
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“…By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system.…”
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“…The numerical results of these estimators are obtained by using numerical integration technique. An application to real data is also given to support the methods.…”
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“…Calculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi–Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. …”
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