Preconditioning for linear systems

SF3584 Preconditioning for linear systems

The problem to determine $x \in R^{n}$ $x\in\mathbb{R}^n$ such that

$A x = b$ $Ax=b$

where $A \in R^{n \times n}$ $A\in\mathbb{R}^{n\times n}$ is maybe the most fundamental problem in computational sciences. In contrast to direct methods, iterative methods (GMRES, CG, BiCG, IDR, etc) provide approximations at each stage in the algorithm. A fast speed of convergence of these approximations is crucial in order to make these methods useful for many large problems. The convergence behavior can often be influenced by transformations or accelerations of the iteration. In this course we learn about several techniques, both general (application independent) techniques and techniques specialized for specific structures or applications, which are constructed to improve the convergence of the iterative methods.

See the book "Preconditioning for linear systems" we authored:

www.preconditioning.se Links to an external site.

See details under: Blocks & planning

The first meeting/lecture will be: Friday Feb. 16 at 10:15 in F11.

Contact the teacher if you are interested and want to be added to the course.

Course learning activities

The course consists of a number of blocks Blocks & planning. The learning activities in the course consist of

Lectures (both by teachers and students), ca 1-2 per block.
problem solving and posing in wiki training area

For each block, some PhD students will be assigned a Block leader role and the other PhD students will have Block student role. All students are expected to pose and answer exercises on the wiki.

Block leaders will specify specific book pages or papers and an introduction presentation of the topic of the block. The block leaders will act as moderators on the wiki and pose $x$ $x$ easy initial exercise questions before the other students start working on the block (where $x \approx 4$ $x\approx4$ ). The block leaders should answer x+y problems and pose more than x+y problems in total.
Block students should pose y questions or more and answer y problems per block, where $LaTeX: y\ge4$ $y\ge4$ . No one should answer their own exercises.

Meetings/lectures: For each block we will have 2 x Z minutes (where $Z \geq 45$ $Z\ge45$ ) lecture given by the block leader. A block is started by a Z minute lecture and ends with a Z minute summary of wiki.

Old info:

http://jarlebring.se/course_training/pmwiki.php?n=Main.Precond Links to an external site.