Approximation with Quasi-Splines de G.H Kirov

Approximation with Quasi-Splines

G.H Kirov

In the theory of splines, a function is approximated piece-wise by (usually cubic) polynomials. Quasi-splines is the natural extension of this, allowing us to use any useful class of functions adapted to the problem.
Approximation with Quasi-Splines is a detailed account of this highly useful technique in numerical analysis.

The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature."

This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.

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Cuprins

Introduction. Restoration of functions of one variable. Restoration of functions of several variables. Some quadrature formulas. Optimal cubature formulas with lattice restrictions for the functional classes ^IH^Ow1w2^I(D^T2) and ^IH^Ow^I(D^O2^I). Approximation of functions with rational quasi-splines. Applications.

Descriere

Approximation with Quasi-Splines is a detailed account of a highly useful technique in numerical analysis.The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature." This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.