Numerical Approximation

  • 申立勇
  • Created: 2014-12-08
Numerical Approximation


Course No.S070102ZJ005

Course CategoryProfessional Basic Course


Prerequisitesadvanced mathematics, linear algebra.

Aims & Requirements

This course is one of the speciality foundation courses for master degree candidates majoring in computational mathematics. It can also be taken as an elective course for those majoring in signal processing, computer graphics and other related fields. This course principally introduces the mathematical foundations, computational methods and current trends of numerical approximation research. Participants of the course are expected to have a command of the basic theories and methods of approximation.

Primary Coverage

Chapter 1 Convolution approximation

Weierstrass approximation theorem; convolution approximation; Dirac sequence.

Chapter 2 polynomial approximation

Polynomial interpolation in one variable; polynomial interpolation in several variables.

Chapter 3 quadratic approximation

Fourier series; system of orthogonal functions; generalized Fourier series; orthogonal polynomials.

Chapter 4 Numerical quadrature

Newton-Cotes formula; Euler-Maclaurin formula; quadrature formulas of Gaussian type.

Chapter 5 Non-linear approximation

Padé approximation; rational approximation; optimal reconstruction.

Chapter 6 Spline functions

Spline functions of a single variable; B-spline functions; multi-variable splines.

Chapter 7 Wavelets

Frame theorymulti-scale analysis; construction of orthogonal wavelet basis.


WANG Renhong, Numerical Approximation, Higher Education Press,1999.


[1] W. Cheney and W. Light, A Course in Approximation TheoryChina Machine Press,2004.

[2] E. M. Stein and R. Shakarchi, Fourier Analysis--An Introduction, Princeton University Press, 2003.

AuthorZhiqiang Xu (Academy of Mathematics and Systems Science)

DateJune, 2009