Publication subTitle :Mathematics in Science and Engineering: A Series of Monographs and Textbooks, Vol. 38
Author: Ahlberg J. H.;Nilson E. N.;Walsh J. L.
Publisher: Elsevier Science
Publication year: 2016
E-ISBN: 9781483222950
P-ISBN(Paperback): 9781483197920
P-ISBN(Hardback): 9781483197920
Subject: O15 algebra, number theory, combinatorial theory;O241 数值分析
Keyword: 一般工业技术
Language: ENG
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Description
The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.