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Excerpt from Theory, Computation, and Application of Exponential Splines
We first outline the theoretical underpinnings of the exponential spline. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data.
We next discuss the numerical computation of the exponen tial spline. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve - fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
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Theory, Computation, and Application of Exponential Splines (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book studies exponential splines, a generalization of cubic splines, exploring their theoretical underpinnings, numerical computation, and wide applications in fields like computational fluid dynamics. The author details the boundary value problem for exponential splines in terms of second derivatives, addressing computational matters such as direct and iterative solutions of the spline equations and spline end conditions. The book also provides a novel parameter selection algorithm that produces shape-preserving interpolants. Furthermore, it delves into the periodic exponential spline, exploring its properties and computational aspects. Along the way, the author offers a wealth of examples that showcase exponential splines' superiority over cubic splines in practical applications, especially in capturing discontinuities without overshoot. This book is a valuable resource for mathematicians, engineers, and scientists seeking to deepen their understanding of exponential splines and their diverse applications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332941971_0
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Theory, Computation, and Application of Exponential Splines Classic Reprint
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