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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Spline Functions and Multivariate Interpolations (Hardcover, 1993 ed.)
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Spline Functions and Multivariate Interpolations (Hardcover, 1993 ed.)
Series: Mathematics and Its Applications, 248
Expected to ship within 10 - 15 working days
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Spline functions entered Approximation Theory as solutions of
natural extremal problems. A typical example is the problem of
drawing a function curve through given n + k points that has a
minimal norm of its k-th derivative. Isolated facts about the
functions, now called splines, can be found in the papers of L.
Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff.
However, the Theory of Spline Functions has developed in the last
30 years by the effort of dozens of mathematicians. Recent
fundamental results on multivariate polynomial interpolation and
multivari ate splines have initiated a new wave of theoretical
investigations and variety of applications. The purpose of this
book is to introduce the reader to the theory of spline functions.
The emphasis is given to some new developments, such as the general
Birkoff's type interpolation, the extremal properties of the
splines and their prominant role in the optimal recovery of
functions, multivariate interpolation by polynomials and splines.
The material presented is based on the lectures of the authors,
given to the students at the University of Sofia and Yerevan
University during the last 10 years. Some more elementary results
are left as excercises and detailed hints are given."
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