Numerical Linear Algebra

Code:

M3024

Acronym:

M3024

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

Active?	No
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	0	Official Study Plan	3	-	6	56	162
L:MA	0	Official Study Plan	3	-	6	56	162

Teaching language

Portuguese

Objectives

Learning outcomes and competences

The student should be able to interpret the Linear Numerical Algebra methods taught, implement them in a computer, test them and use them in problem solving.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of Linear Algebra, and computational programming in any language.

Program

I – Numerical resolution of systems of linear equations and numerical computation of inverses of matrices. Vector and matrix norms. Gram-Schmidt orthonormalization. Conditioning and stability. Condition numbers. Matrix types. Elementary matrix and transformations. Triangular systems. Gauss elimination and LU factorization with pivoting. Computation of inverse matrix. Positive definite matrix. Cholesky method. QR decomposition. Iterative methods of Jacobi and Gauss-Seidel. Applications.

II – Numerical computation of eigenvalues and eigenvectors. Gersgorin location. Direct and inverse power methods. Orthogonal matrix. Singular value decomposition (SVD). Pseudoinverse. Least square solution of linear systems. QR-algorithms. Applications.

Mandatory literature

William Ford; Numerical linear algebra with applications. ISBN: 978-0-12-394435-1
Alfio Quarteroni, Fausto Saleri; Calculo Científico com Matlab e Octave, Springer, 2007. ISBN: 978-88-740-0717-8

Teaching methods and learning activities

Software

GNU Octave
Matlab

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Prova oral	25,00
Teste	50,00
Trabalho escrito	25,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Apresentação/discussão de um trabalho científico	1,00
Elaboração de projeto	25,00
Estudo autónomo	53,00
Frequência das aulas	56,00
Trabalho escrito	2,00
Trabalho laboratorial	25,00
Total:	162,00

Eligibility for exams

Realization of a project with report and oral presentation.

Calculation formula of final grade

Test with computacional part: 50%
Report: 25%
Oral presentation: 25%

Classification improvement

Only in the part corresponding to the test.