Kurt Frischmuth: Intro to Numerics

Kurt Frischmuth

Lecture

Introduction to Numerical Analysis

for Computational Science and Engineering




Abstract

The lecture covers basic numerical methods such as
interpolation, approximation, equation solving, matrix decompositions and eigenvalue problems.
Concepts like stability, consistency, condition and numerical cost will be discussed as well.

The lecture comes with a tutorial.
It will be essential to implement methods and test them on examples - individually.
Skills in calculus, algebra, computer science and programming are required (on BSc level), but not part of this subject.



Bibliography

selected books



Examination

time: March 7, 2018
partial and inofficial results:
examination of 07.03.2018

before you complain about too few points, please think:
  1. Did you calculate the wanted root normally and by rounding step-by-step to 5 digits?
    (You lose accuracy when taking the difference between b and the root)
    Did you get the difference and calulate from that the relative error?
    Did you improve the inaccurate result by a Newton step?
  2. Simple iteration meant to calculate a new x from the second equation and a new y from the first one.
    Did you do this, for the requested number of iterations?
    Did you estimate the Lipschitz constant and the requested number of steps?
  3. Did you calculate the T-values correctly, obtain from there the Romberg improvements?
    Did you use the proper error estimate to get the required number of stripes?
  4. You were supposed to make use of the symmetry of the matrix.
    Did you split it into factors as instructed, and did you use the decomposition to find the solution?
    Did you find the critical parameter?
  5. Did you calculate the k-values properly, and did you evaluate the required approximations correctly?
    Did you obtain and compare the errors?
Please notice that just copying material from lecture notes, exercises or books does not count much at an open book examination.

inspection of examination papers of March 11, 2018, will be possible April 11, 2018, from 2 to 3 pm at my office

Remember that stealing time means bad karma!

As second date for those unable to come on April 11, I set May 9, 11 am.



© Kurt Frischmuth, April 3, 2018.