Kurt Frischmuth: Intro to Numerics
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Kurt Frischmuth

### Lecture

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*Introduction to Numerical Analysis*

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for Computational Science and Engineering

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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.

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Bibliography

selected books

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Examination

time: March 7, 2018

partial and inofficial results:

examination of 07.03.2018

before you complain about too few points, please think:
- 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?
- 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?
- 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?
- 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?
- 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.