Numerical Analysis Aug-Dec 2013
For latest and updated codes, see https://github.com/cpraveen/na
Students
- Abhrojyoti Sen
- Amrita Ghosh
- Aniket Bhanja
- Arka Mallick
- Arnab Roy
- Arunima Bhattacharya
- Debabrata De
- Debdeep Bhattacharya
- Manish Kumar Singh
- Manmohan
Reference texts
- K. Atkinson, Introduction to Numerical Analysis, Wiley
- David Kincaid and E. Ward Cheney, Numerical Analysis: Mathematics of scientific computing
Computer programs
Codes are available here
https://github.com/cpraveen/na2013
You can also get them using git
git clone https://github.com/cpraveen/na2013
Computer arithmetic
- Store 1/10 and print it to see the conversion of real number to floating number
- Demonstration of unit round
- Example of overflow error and how to avoid it
- Errors due to subtracting nearly equal quantities
- Sensitivity of polynomial roots
- Unstable iterations
- Unstable iterations: ODE example
Root finding
- Bisection method: matlab, python
- Newton method: matlab, python
Interpolation
- Condition of vandermonde matrix: matlab
- Interoplate nice function like cos(x) on uniform data: matlab
- Interpolate on uniform and chebyshev points, Runge phenomenon: matlab
- Interpolate abs(x) on uniform and chebyshev points: matlab
- Interpolation to show Runge phenomenon, barycentric lagrange formula: python
- Behaviour of interpolation error on uniform and chebyshev points: matlab
- Behaviour of newton forward differences under roundoff error: matlab
- Adaptive piecewise P1 interpolation: matlab
- Trigonometric interpolation of periodic function: matlab
- Comparison of trigonometric and polynomial interpolation: matlab
- Convergence of trigonometric interpolation: matlab
Solving ODE
- Euler method, convergence test: python
- Euler method, convergence test: python
- Euler method, instability example: python
- Trapezoidal method, convergence test: python
- Absolute stability domains of AB, AM, BDF schemes: python
- Example of stiff ODE: python
- ODE with periodic solution, quadratic invariant: python