Numerical Linear Algebra and Optimization in Engineering

Basics of Linear Algebra; Matrix decomposition - LU, LDU, QR and Cholesky factorization; Householder reflection, Givens rotation; Numerical implications of SVD; Numerical Solution for Linear Systems; Algorithm Stability; Problem Conditioning; Pivoting and scaling; Least Square Solutions; Numerical Matrix eigenvalue methods; Sparse Systems; Iterative methods for large systems; Krylov, Arnoldi, Lanczos methods; Numerical Optimization techniques - Conjugate gradient method, Linear and quadratic programming, Spectral and Pseudo-spectral methods.