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.
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