ELL 800: Numerical Linear Algebra

Syllabus

• Basics of linear algebra.

• Floating point arithmetic.

• Vector Norms and Induced Matrix Norms

• Linear system of equations, condition number, Perturbation in A and b.

• Matrix Factorizations: LDU, Cholesky, QR , Singular Value Decomposition.

• Eigenvalues, Eigenvectors, Invariant Spaces.

• Eigenvalue sensitivity.

• Eigenvalue-Eigenvector Computation, Arnoldi iteration, Implicitly restarted Arnoldi iteration.

• SVD Computation

• Iterative methods for Ax=b, Conjugate Gradient Method

Reference Books

• Golub, Gene H., and Charles F. Van Loan. Matrix computations. Vol. 3. JHU Press, 2012.

• Watkins, David S. Fundamentals of matrix computations. Vol. 64. John Wiley & Sons, 2004.

• Trefethen, Lloyd N., and David Bau III. Numerical linear algebra. Vol. 50. Siam, 1997.