# 2D1290, Advanced Numerical Analysis 2006, 4 poäng

Formal description, that is, the text in the studiehandbook.
Most recent changes by Ninni Carlsund on 6 januari 2007.

## Latest news - change of schedule.

The lecture on Thursday April 27 is moved to Thursday May 4, 8-10 o'clock. There will also be an extra lecture on Thursday May 11, 8-10 o'clock. Classroom is 1635 (on floor 6 in E-house).

The first lecture was Thursday 16 March 2006, in classroom D33. For further details, see the KTH-schedule

## General Description and Aim

The course is devoted to the introduction of advanced numerical methods in Scientific Computing for large scale applications. The aim of the course is to give the students an introduction to the construction principles of advanced numerical methods so that they will be able to understand, use, and develop efficient algorithms for large scale problems.

## Topics

1. Fast Multi-pole Methods. The essential aim is to show that using cleverly chosen approximations and divide- and -conquer techniques an intentionally $O(n^2)$ computational process can be reduced to $O(\log\frac{1}{\eps}n\log n)$ complexity if $\eps$ denotes a given (desired) precision.
2. Krylov-type Iteration Methods. A well-established technique for the solution of large sparse linear systems of equations with a symmetric and positive definite coefficient matrix is the (preconditioned) conjugate gradient method. Here we will show how it can be extended to more general and even nonlinear problems.
3. Multilevel Methods. These methods are well-known as efficient tools for the iterative solution of linear (and nonlinear) systems of equations arising while discretizing partial differential equations. Here, we will start from the classical viewpoint and introduce some recent developments which lead to very efficient implementations of pde solvers.

## Classes

Lectures/exercises: 8 lectures, each lasting 2 hrs.

The first lecture is Thursday 16 March 2006, in classroom D33. For further details, see the KTH-schedule

## Course requirements

Written or oral examination (2 cr.); Computer assignments (2 cr.)

## Recent course: period 4 05/06

Other courses at Nada for D-level students.

### Previous round: 1999/00

Some examples of the written examinations are Exam 1998 and Exam 1999. Exam 2000,and solutions, Exam 2001,and solutions, Exam 2002,and solutions.

## Course evaluation

To continuosly update the courses we encourage the students to comment them. Please help us by, towards the end of the course fill out a course evaluation form. (The evaluation form will be posted here by the end of the course.) And these are the conclusion/evaluations of previous years: 1999/2000, 2000/2001, 2001/2002, 2002/2003.