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Approximation with quasi-splines

Author: G Kirov
Publisher: Bristol ; Philadelphia : Institutes of Physics Publishing, ©1992.
Edition/Format:   Print book : EnglishView all editions and formats

Describes various approximation theorems and optimization methods. This book offers an account of this useful technique in numerical analysis. It is suitable for various practitioners of the methods  Read more...


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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: G Kirov
ISBN: 0750301813 9780750301817
OCLC Number: 24952574
Description: vi, 247 pages : illustrations ; 24 cm
Contents: Introduction. Motivation. Moduli of continuity. Integral and averaging moduli. Spaces and classes of functions. Statement of the extremal problem. Meshes and their characteristics. Survey of the results. 2: Recovery of Functions of One Variable: Optimization theorem. The standard function. The error of the best method in ^IH^Ow. Optimal methods in ^IH^Tw. Recovery of functions of the classes ^IW^Tr^IH^Tw. 3: Recovery of Functions of Several Variables: Best method for recovery of functions of several variables. An optimal method for recovery of functions of several variables. 4: Some Quadrature Formulas: The best quadrature formula for functions of the chass ^IH^Ow. Optimal quadrature formulas for functions of the class ^IH^Ow. An estimation for the error of optimal quadrature formulas for individual functions in ^IH^Ow. Optimization of the quadrature formula of Niederreiter type for the function classes ^IW^OrH^Ow. 5: Optimal Cubature Formulas with restrictions on the Lattice for the Function Classes ^IH^Ow1w2^I(D^T2) and ^IH^Ow^I(D^T2): Best cubature formula. Optimal cubature formulas for the classes ^IH^Ow1w1^I(D^T2) and ^IH^Ow^I(D^T2). 6: Approximation of Functions by Rational Quasi-Splines: Definition of the basic quasi-splines. Examples. Elementary properties of the basic quasi-splines. Convexity of the basic quasi-splines. Some properties of the fundamental rational quasi-splines. Approximation of functions by rational quasi-splines in uniform metrics. Approximation of functions by rational quasi-splines in integral metrics. 7: Applications; Representation of the derivatives of the basic quasi-splines. Monotonic sequences of basic quasi-splines. Properties of the solutions of Problem C. non-analyticity of the function ^I^D*l(x). Localization of the zeros of the derivatives of the function ^I^D*l(x). Tabulating integral reoresentation and central moments of the function ^I^D*l(x). References. Author index. Subject index.
Other Titles: Quasi-splines.
Responsibility: G.H. Kirov.
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