Academic year 2016/2017 PhD program in Mathematics UC-UP Department of Mathematics Faculty of Science and Technology, University of Coimbra Teacher: Adérito Araújo

Class	Monday	Tuesday	Wednesday	Thursday	Friday
		11:00-13:00 Room: 2.5		11:00-13:00 Room: 2.5
Attendance	Monday	Tuesday	Wednesday	Thursday	Friday
		14:00-15:00 Office: 5.1

1. Introduction

2. Basic operations and norms

3. Orthogonality and the SVD

4. Introduction to error analysis

5. Linear systems

6. Linear Least Squares

7. Eigenvalue problems

8. Iterative methods

9. Sparse matrices

10. Introduction to High-Performance Computing

11. Projects and applications

• L. N. Trefethen, D. Bau. Numerical Linear Algebra. SIAM 1997.

• J. W. Demmel. Applied Numerical Linear Algebra. SIAM 1997.
  Also aimed at a first year graduate audience, but has a more practical flavor than the main text.
• G. H. Golub, C. F. Van Loan. Matrix Computations. John Hopkins University Press 1996.
  Very complete, if not encyclopedic, book on matrix computations.
• Yousef Saad. Iterative Methods for Sparse Linear Systems. PWS Publishing, 1996. Comprehensive work on methods for iterative methods.

• E. Anderson et al. LAPACK Users' Guide, SIAM 1999 (3rd Edition).
  Describes widely used library of dense numerical linear algebra software.
• R. Barrett et al. Templates for the Solution of Linear Systems, SIAM, 1994.
  Describes standard Krylov-space iterative methods for solving Ax = b, with guidance on choosing and algorithm and software.
• Z. Bai et al. Templates for the Solution of Algebraic Eigenvalue Problems. SIAM, 2000.
  Gives a unified overview of theory, algorithms and practical software for eigenvalue problems.

• A. Bjorck. Numerical Methods for Least Squares Problems. SIAM 1996.
  Comprehensive work on methods for linear least squares problems.
• W. Briggs. A Multigrid Tutorial, SIAM, 1987.
  A good introduction to multigrid methods.
• N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM 2002 (2nd edition).
  Comprehensive rounding error analysis for linear equations and least squares problems.

The midterm final exam are in the following dates.

Hour	Midterm exam	Hour	Final exam
14:30	April 2015	14:30	June 2015