DN2290 Advanced Numerical Analysis, spring 2008
(avnum08) Credits: 4 p = 6 hp
Formal description,
that is, the text in the study-handbook.
Most recent changes by
Ninni Carlsund on 17 oktober 2008.
Teaching and Examination
There will be eight 2-hour lectures during April and May,
where the theory of the methods will be presented and discussed.
The first lecture will be in week 14, 2008.
Examination is by 4 computer assignments
(or by 1 large computer assignment)
and one written examination.
The computer assignments are done in parallel to the lectures
and the concluding written examination will be on June 3rd 2008,
at 8 o'clock in room D35.
The exact times and dates will be decided when the course starts,
see below.
ReExam: Those interested, contact me.
If you want to take the written exam, contact me, so we can agree on a date.
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
- 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.
- 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.
- 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 in week 14, 2008.
Preliminary times and dates are
- Monday 31 March at 10-12 in room 1537 (NADA/CSC, floor 5).
- Monday 7 April at 10-12 in room 1537.
- Thursday 10 April at 10-12 in room 1537.
- Monday 14 April at 10-12 in room 1537.
- Monday 21 April at 10-12 in room 1537.
- Monday 28 April at 10-12 in room 1537.
- Monday 5 May at 10-12 in room 1537.
- Monday 12 May at 10-12 in room 1537.
- EXAM: Tuesday 3 June at 8-13 in room D35.
Course requirements
Written or oral examination (2 cr. = 3hp); Computer assignments (2 cr. = 3hp)
Other courses at
CSC/Nada for D-level students.
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.
Older written exams
The last exam was in June 2006.
For older exams, see
the old webpage
of the course.
Up to Nada course list.
Responsible for this page: Ninni Carlsund <ninni@nada.kth.se>
Latest change October 17, 2008
Technical support: <webmaster@nada.kth.se>