Large Dimensional Matrix Computations

Code:

PRODEM093

Acronym:

CMGD

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2009/2010 - 1S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Doctoral Program in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEM	0	Syllabus since 2009/10	1	-	6,5	60	175,5

Teaching language

Portuguese

Objectives

This course unit may be taught in Portuguese, English or French, depending on students’ nationality.

Program

Descriptive summary:
1- Resolution of large dimensional systems
1.1 – Sparse matrix techniques. Structured matrices issued from real life problems
1.2 - Krylov subspace methods, namely conjugate gradient method, GMRES (generalized minimal residuals) method; brief theoretical description and convergence properties; advantages, disadvantages and applicability. Preconditioning.
1.3 – Multigrid methods.
2 – Methods for the computation of eigenvalues and eigenvectors of large dimensional problems:
2.1 – Lanczos and Arnoldi methods. Brief theoretical description and details of implementation; Existing software.
2.2 - SVD (single value decomposition).

Teaching methods and learning activities

This course unit is based on Matlab because of its usefulness in Linear Algebra and graphic representation.

Evaluation Type

Distributed evaluation with final exam

Observations

This course unit may be taught in Portuguese, English or French, depending on students’ nationality.