The exhaustive list of topics in Matrix Computations in which we provide **Help with Homework Assignment** and **Help with Project** is as follows:

Floating Point Computation:

- Matrix computations.
- Matrices and vectors, Norms, Singular value decompositions.
- Floating point computations, IEEE floating point arithmetic, analysis of roundoff errors. Pitfalls of floating point computations.

Solution Of Linear Systems:

- Concept of stability and ill-conditioning, Generic sensitivity analysis, Condition numbers, Backward and forward stability.
- Solution of linear systems, triangular and banded systems, Gaussian elimination, Pivoting, Stability of Gaussian elimination, Cholesky factorization.

Solution Of Least Squares Of Problem:

- Orthogonal matrices, Rotators and Reflectors, Gram-Schmidt process, QR factorizations, Stability of Householder QR factorization.
- Solution of Least Squares Problem by QR method, The SVD and the Least Squares Problem, Sensitivity of the Least Squares Problem.
- Solution Of Eigenvalue Problem And Computation Of SVD:
- Eigenvalue problems, Overview of eigenvalue algorithms, Sensitivity analysis of eigenvalue problems.
- Power, inverse power and Rayleigh quotient iterations; Reduction to Hessenberg and Tridiagonal forms.
- QR algorithm with and without shifts, convergence of the QR algorithm.
- Implicit QR algorithm with Wilkinson’s shift.
- Other eigevalue algoritms (Jacobi, bisection, divide and conquer).
- Reduction to bi-diagonal form, Computing the SVD.

Iterative Methods For Solution Of Linear Systems:

- Iterative methods, Jacobi, Gauss-Seidel and successive over relaxation methods.
- Generic Krylov process, Implicit restarts, The Arnoldi iteration, The Lanczos iteration.
- Conjugate gradient method, Preconditioning.