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Mathematics of Approximation (Hardcover, 2012 ed.)
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Mathematics of Approximation (Hardcover, 2012 ed.)
Series: Mathematics Textbooks for Science and Engineering, 1
Expected to ship within 12 - 17 working days
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The approximation of a continuous function by either an algebraic
polynomial, a trigonometric polynomial, or a spline, is an
important issue in application areas like computer-aided geometric
design and signal analysis. This book is an introduction to the
mathematical analysis of such approximation, and, with the
prerequisites of only calculus and linear algebra, the material is
targeted at senior undergraduate level, with a treatment that is
both rigorous and self-contained. The topics include polynomial
interpolation; Bernstein polynomials and the Weierstrass theorem;
best approximations in the general setting of normed linear spaces
and inner product spaces; best uniform polynomial approximation;
orthogonal polynomials; Newton-Cotes, Gauss and Clenshaw-Curtis
quadrature; the Euler-Maclaurin formula; approximation of periodic
functions; the uniform convergence of Fourier series; spline
approximation, with an extensive treatment of local spline
interpolation, and its application in quadrature. Exercises are
provided at the end of each chapter
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