Interpolation and Approximation by PolynomialsSpringer Science & Business Media, 6 avr. 2006 - 312 pages This book is intended as a course in numerical analysis and approximation theory for advanced undergraduate students or graduate students, and as a reference work for those who lecture or research in this area. Its title pays homage to Interpolation and Approximation by Philip J. Davis, published in 1963 by Blaisdell and reprinted by Dover in 1976. My book is less g- eral than Philip Davis’s much respected classic, as the quali?cation “by polynomials” in its title suggests, and it is pitched at a less advanced level. I believe that no one book can fully cover all the material that could appearinabookentitledInterpolation and Approximation by Polynomials. Nevertheless, I have tried to cover most of the main topics. I hope that my readers will share my enthusiasm for this exciting and fascinating area of mathematics, and that, by working through this book, some will be encouraged to read more widely and pursue research in the subject. Since my book is concerned with polynomials, it is written in the language of classical analysis and the only prerequisites are introductory courses in analysis and linear algebra. |
Table des matières
1 | |
Best Approximation | 49 |
Numerical Integration | 119 |
Peanos Theorem and Applications | 147 |
Multivariate Interpolation | 163 |
Splines | 215 |
Bernstein Polynomials | 247 |
Properties of the qIntegers | 291 |
305 | |
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Expressions et termes fréquents
abscissas algorithm B-splines Bernstein polynomials Bn(f Chebyshev polynomials coefficients column completes the proof convex deduce defined denote derivative difference formula divided difference equioscillation error term Euler-Maclaurin formula evaluate Example expressed f(xo factor follows forward difference function ƒ fundamental polynomial Gaussian rule given function induction inequality integrand integration rule interpolating polynomial interval of support knots Legendre polynomials Let us write linear equations linear functional lines matrix minimax approximation minimax polynomial monomials monotonically nonnegative nonzero obtain orthogonal partitions Pn(x polynomial of degree polynomial q Problem q-difference q-integers recurrence relation Remez algorithm respectively result sequence set of points Simpson's rule spline spline of degree square norm Theorem three-pencil mesh ti+1 ti+2 ti+n+1 totally positive trapezoidal rule triangle truncated power function Vandermonde Vandermonde matrix vector verify weight function zero