Theories and Algorithms of Numerical Approximation

  • 申立勇
  • Created: 2014-12-08
Theories and Algorithms of Numerical Approximation

Course No.S070104ZJ008                

Course CategoryProfessional Basic Course

Period/Credits40/2

PrerequisitesHigher calculation, linear algebra

Aims and Requirements

This course is the basic course of computational mathematics and computer science as well as other needs numerical calculation of the postgraduates. This course covers the basic methods of numerical calculation, calculation methods and mathematical theoretical basis for the calculation of the relevant professional. Main contents include: error, interpolation, approximation theory, numerical differentiation and integration; matrix norm theory, the solution of linear equations direct and iterative methods, nonlinear equations,  eigenvalues ,  vector calculus, ordinary differential equation solving and so on.
Through this course, students can master the basic theories and methods of numerical approximation.

Primary Coverage

Chapter 1,  concept of error, causes and reduction.

Chapter 2,  concept of interpolation, polynomial interpolation, remainder of the interpolation polynomial and convergence, orthogonal polynomial, best square approximation, expanding by Chebyshev polynomial.

Chapter 3,  consistent approximation in function space, existence and uniqueness, the approximate order, class of approximate functions.

Chapter 4,  Numerical differentiation, numerical integration, difference, intepolation differentiation and integration, Newton-cotes integration.

Chapter 5,  Normal of vectors and matrices, conditions of matrix, convergence matrix, QR decomposition.

Chapter 6,   Solving linear and nonlinear equations, elimination method, LU decomposition, SVD method, iterative algorithm of Jacobi, Gauss-Seidel, Newton.

Chapter 7,   Soving ODE, Euler formula,  Runge-Kutta method, implicit iteration schemes

References:

1.Feicheng Xie, Numerical analysis, Press of University of Science and Technology of China, 1995.         

2.Renhong Wang, Numerical approximation, High Education Press, 2003

 

Author: Liyong Shen

Date: June,2009