On Interpolating Cubic Splines with Equally-spaced Nodes PDF Download

Author: F. Schurer
Publisher:
ISBN:
Category : Spline theory
Languages : en
Pages : 28

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Author: Gary D. Knott
Publisher: Springer Science & Business Media
ISBN: 1461213207
Category : Computers
Languages : en
Pages : 247

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A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

Author: Gheorghe Micula
Publisher: Springer Science & Business Media
ISBN: 9401153388
Category : Mathematics
Languages : en
Pages : 622

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The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.

Author: Thomas Nall Eden Greville
Publisher:
ISBN:
Category : Curve fitting
Languages : en
Pages : 14

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A table is given to facilitate the calculation of the parameters of the interpolating third-degree natural spline function for n given data points (n> 2) with equally spaced abscissas. The use of the table is described and the correctness of the algorithm is demonstrated. (Author).

Author: Peter J. Olver
Publisher: Springer
ISBN: 3319910418
Category : Mathematics
Languages : en
Pages : 702

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This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Author: P. M. Prenter
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 342

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Introduction ideas; Lagrangian interpolates; Hermitian interpolates; Polynomial splines and generalizations; Approximating functions of several variables; Fundamentals for variational methods; The finite element method; The method of collocation; Index.

Author: Nicolò Barbero
Publisher: Springer Science & Business Media
ISBN: 8847052203
Category : Science
Languages : en
Pages : 349

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This book is intended for undergraduates and young researchers who wish to understand the role that different branches of physics and mathematics play in the execution of actual experiments. The unique feature of the book is that all the subjects addressed are strictly interconnected within the context of the execution of a single experiment with very high accuracy, namely the redetermination of the Avogadro constant NA, one of the fundamental physical constants. The authors illustrate how the basic laws of physics are applied to describe the behavior of the quantities involved in the measurement of NA and explain the mathematical reasoning and computational tools that have been exploited. It is emphasized that all these quantities, although pertaining to a specific experiment, are of wide and general interest. The book is organized into chapters covering the interaction of electromagnetic radiation with single crystals, linear elasticity and anisotropy, propagation of thermal energy, anti-vibration mounting systems, and data analysis and B-spline interpolation. An essential feature is the focus on the role of Mathematica, an invaluable, fully integrated software environment for handling diverse scientific and technical computations.

Author: Grace Wahba
Publisher:
ISBN:
Category :
Languages : en
Pages : 42

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Statistical properties of the histospline density estimate of Boneva-Kendall-Stefanov-Schoenberg are found. This density estimate is the derivative of a cubic spline of interpolation to the sample cumulative distribution at equally spaced points. The spacing of these points is chosen in an optimal manner. The boundary values of the spline are estimated from the data. It is shown that the mean square convergence rate of this density estimate at a point achieves the best obtainable rate. (Author).

Author: K. Böhmer
Publisher: Springer
ISBN: 3540380736
Category : Mathematics
Languages : en
Pages : 427

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Author: Helmuth Späth
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 214

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