### Math 6610: Analysis of Numerical Methods I

#### Textbook and References

Main Textbook: Trefethen and Bau, Numerical Linear Algebra, SIAM, 1997

References:

Golub and Van Loan, Matrix Computations, 3rd Ed, 1996;

E. Suli and D. Mayers, An Introduction to Numerical Analysis, Cambridge 2003

Carl Meyer, Matrix Analysis and Applied Linear Algebra, SIAM 2000

A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, (Texts in Applied Mathematics), 2006

#### The course

Math 6610 is the first semester of a two semester graduate-level sequence in numerical analysis. The first semester focuses primarily on numerical linear algebra. The second semester focuses primary on numerical methods for solving differential equations.

#### Homework

Homework will be assigned and collected, and will include theoretical analysis and computational assignments. The computational part should be done using MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good place to begin and is available in Adobe PDF format.

#### 6610 Overview of Some Topics:

i) Some familiar fundamentals, ii) SVD, iii) Projections, iv) QR factorization, v) Application of QR to Least Squares problem, vi) Finite-precision arithmetic, stability of algorithms, and sensitivity of problems (conditioning), vii) Gaussian elimination and its variants for solving a linear system, viii) Eigenvalue problems and algorithms, ix) Iterative methods for linear systems: classical methods (Jacobi, Gauss-Seidel, Successive Overrelaxation (SOR)); Conjugate Gradient; Arnoldi/Lanczos Iterations; GMRES, Other Krylov Subspace Methods

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.

#### Grading: Homework 65% and one Final Written Exam (December 19, 10:30am-12:30 pm during final's week) 35%

Please e-mail me if you would like copies of the previous homework for Fall 2014.

• Homework 1

• Homework 2

• Homework 3
• Homework 4

• Homework 5