Literature

Apart from the textbook

Cleve Moler. Numerical Computing with MATLAB, ISBN: 978-0-89871-660-3, https://www.mathworks.com/moler/index_ncm.html

which we will use for the course, there are various other nice books and lecture notes on the topic.

Among others, there are

• Gene H. Golub and Charles F. Van Loan. Matrix computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, fourth edition, 2013.
• Nicholas J. Higham. Accuracy and stability of numerical algorithms. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2002.
• Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. Numerical mathematics, volume 37 of Texts in Applied Mathematics. Springer-Verlag, Berlin, second edition, 2007.
• Endre Süli and David F. Mayers. An introduction to numerical analysis. Cambridge University Press, Cambridge, 2003.
• Charles F. Van Loan: Introduction to Scientific Computing. Prentice Hall, 1997. Link to book webpage with MATLAB scripts

(The list might be extended over the course of the semester)

Additional reading material:

1. Computer Arithmetic and Errors:

• David Goldberg's paper "What Every Computer Scientist Should Know About Floating-Point Arithmetic"
• Some famous examples of Roundoff error: Patriot Missile Failure, Ariane 5
• Michael L. Overton : Numerical Computing with IEEE Floating Point Arithmetic (the electronic version should be accessible for free via the UMD library)

2. Solution of Linear Systems of Equations:

• Partial v.s. complete pivoting: N.J. Higham and D.J. Higham, Large growth factors in Gaussian elimination with pivoting, SIAM J. Matrix Analysis and Appl., 10 (1989), pp. 155-164

3. Interpolation:

• Some m-files for Vandermonde interpolation
• Some matlab scripts to demonstrate errors in polynomial interpolation.