“…Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. …”
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“…The text covers useful numerical methods, including interpolation, Simpson’s rule on integration, the Gauss elimination method for solving systems of linear algebraic equations, the Runge-Kutta method for solving ordinary differential equations, and the search method in combination with the bisection method for obtaining the roots of transcendental and polynomial equations. …”
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“…Parmi les questions traitées dans le manuel citons : opérations sur les nombres approchés, calcul des valeurs d'une fonction, résolution approchée et numérique des équations algébriques et transcendantes, méthodes numériques de l'algèbre linéaire, interpolation des fonctions, dérivation et intégration rapprochée, éléments de la méthode de Monte-Carlo.…”
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“…The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. .…”
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“…For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. …”
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“…From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.…”
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“…The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.…”
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“…The LHCf experiment will have the possibility to perform direct measurements of the very-forward neutral particle production and the nuclear modification factor without the need of an interpolation of the results in proton-proton and proton-lead collisions. …”
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“…Angularities are a general class of event shapes which depend on a continuous parameter \(b>-1\) that interpolates between recoil-insensitive observables like thrust and observables that are maximally sensitive to recoil effects like jet broadening. …”
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“…The current method, based on linearly-interpolated optics functions over a small set of matched optics and parabolic time-domain segments, introduces non-zero beta-beating and it is not optimal in time. …”
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“…Geographic modeling can help in the interpretation of environmental sampling data associated with airborne concentration or deposition, and can act as a sophisticated interpolator for such data, allowing values to be assigned to locations between points where the data have actually been collected. …”
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“…In particular, a set of solutions describes generalized gravitating kinks where the scalar field interpolates between two different minima of the potential. …”
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“…We then detail glycerol measurement in conditioned media and its interpolation. For complete details on the use and execution of this protocol, please refer to Coskun et al.(1)…”
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“…A global potential energy surface (PES) for the electronic ground state of the Na + HF reactive system is constructed by three-dimensional cubic spline interpolation of 37 000 ab initio points obtained using the multireference configuration interaction method including the Davidson's correction (MRCI + Q) with auc-cc-pV5Z basis set. …”
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“…Our results provide further evidence for the intimate link between the segmentation processes that occur in conditions of transparency and occlusion, and the interpolation processes involved in the formation of amodally completed surfaces.…”
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“…A novel normalization and interpolation algorithm is proposed to convert an ECG signal into multiple template cycles, which are comparable between any two ECGs, no matter the sampling rates or health status. …”
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“…A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. …”
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“…The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. …”
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“…This data was used for computer simulation based model of SR machine, “Selecting Best Interpolation Technique for Simulation Modeling of Switched Reluctance Machine” [1], “Modeling of Static Characteristics of Switched Reluctance Motor” [2]. …”
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“…Sample are quantified by interpolation from the calibration curve and reported in µg/mL. …”
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