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Instructor Spring 2019: Paul Constantine

Textbooks

Lectures will be based on the following text:

• Numerical Methods in Matrix Computations by Ake Bjorck, Springer 2015
• This text is available in electronic format through the university library; a low-cost black and white paperback is also available for order through the university library.

Supplementary material may be drawn from the following two texts:

• Matrix Computations by Gene Golub and Charles van Loan, Johns Hopkins 2013 (third or fourth editions)
• Iterative Methods for Sparse Linear Systems by Yousef Saad, SIAM 2003 GvL is a classic reference. A pdf copy of Saad's book is available free online.

Course Goals

We will develop and analyze algorithms for solving nonsingular linear systems of equations and least-squares problems, and for computing eigenvalues and eigenvectors. Along the way we will discuss classical matrix factorizations including (but not limited to) LU, Cholesky, QR, and SVD. We will cover direct and iterative methods for small and large, dense and sparse matrices. Broadly speaking, we hope to cover the material in sections 1.1{1.4, 2.1{2.4, 3.1{3.5, and 4.1{4.2 from Bjorck. Time permitting, extra topics may be covered based on student interest.

Grade determination

The final course grade will be determined by a weighted average of class participation (30%), in-class/take-home assignments (50%), and exams (20%).

• Homework: You may work in groups on the assignments, but each student must prepare and submit their own solutions. Assignments will include a mix of analysis and simulation; proficiency with Matlab or a similar computing language is required. You do need to submit your code.
• Exams: There will be 3 in-class exams and an optional final. Exams will include a mix of true/false and proofs. Notes, textbooks, and calculators (which will be useless. . . ) will be allowed on the exams, but not computers or phones or neighbors!