To introduce modern approximation techniques; to explain how, why, and when they can be expected to work; and to provide a foundation for further study of scientific computing.

To introduce modern approximation techniques; to explain how, why, and when they can be expected to work; and to provide a foundation for further study of scientific computing.

課程概述
Round-off error; algorithms and convergence; the bisection method; the
fixed-point iteration; the Newton method; accelerating convergence; the
Muller method; Lagrange interpolation; Newton divided differences; Hermite
interpolation; cubic spline interpolation; numerical differentiation;
Richardson extrapolation; numerical integration; composite numerical
integration; Romberg integration; Gaussian quadrature; adaptive quadrature
method; initial value problem; the Euler method; higher-order Taylor method;
the Runge-Kutta methods and so on.

Course Overview
Round-off error; algorithms and convergence; the bisection method; the
fixed-point iteration; the Newton method; accelerating convergence; the
Muller method; Lagrange interpolation; Newton divided differences; Hermite
Interpolation; cubic spline interpolation; numerical differentiation;
Richardson extrapolation; numerical integration; composite numerical
integration; Romberg integration; Gaussian quadrature; adaptive quadrature
method; initial value problem; the Euler method; higher-order Taylor method;
the Runge-Kutta methods and so on.

R.L. Burden, J.D. Faires and A.M. Burden , Numerical Analysis, 10th edition, Cengage Learning, 2016

R.L. Burden, J.D. Faires and A.M. Burden, Numerical Analysis, 10th edition, Cengage Learning, 2016