Numerical Analysis 2013

Reference texts

• 1. K. Atkinson, Introduction to Numerical Analysis, Wiley

  2. David Kincaid and E. Ward Cheney, Numerical Analysis: Mathematics of scientific computing

Computer programs

Some of the programs are hosted on googlecode. To download the source code, click on the link to the right which says "View raw file". Then save the file to your computer.

Computer arithmetic

1. Store 1/10 and print it to see the conversion of real number to floating number

2. Demonstration of unit round

3. Example of overflow error and how to avoid it

4. Errors due to subtracting nearly equal quantities

5. Sensitivity of polynomial roots

6. Unstable iterations

7. Unstable iterations: ODE example

Root finding

• 1. Bisection method: matlab, python

  2. Newton method: matlab, python

Interpolation

• 1. Condition of vandermonde matrix: matlab

  2. Interoplate nice function like cos(x) on uniform data: matlab

  3. Interpolate on uniform and chebyshev points, Runge phenomenon: matlab

  4. Interpolate |x| on uniform and chebyshev points: matlab

  5. Interpolation to show Runge phenomenon, barycentric lagrange formula: python

  6. Behaviour of interpolation error on uniform and chebyshev points: matlab

  7. Behaviour of newton forward differences under roundoff error: matlab

  8. Adaptive piecewise P1 interpolation: matlab

  9. Trigonometric interpolation of periodic function: matlab

  10. Comparison of trigonometric and polynomial interpolation: matlab

  11. Convergence of trigonometric interpolation: matlab

Solving ODE

• 1. Euler method, convergence test: python

  2. Euler method, convergence test: python

  3. Euler method, instability example: python

  4. Trapezoidal method, convergence test: python

  5. Absolute stability domains of AB, AM, BDF schemes: python

  6. Example of stiff ODE: python

  7. ODE with periodic solution, quadratic invariant: python