Module - 1:Some basics of Linear Algebra :- Vector spaces, Linear transformations, eigen values and eigen vectors.
Module - 2:Matrix norm, Sensitivity analysis and condition numbers, Linear systems, Jacobi, Gauss-Seidel and successive over relaxation methods, LU decompositions, Gaussian elimination with partial pivoting, Banded systems, positive definite systems, Cholesky decomposition – sensitivity analysis, Gram- Schmidt orthonormal process, Householder transformation, QR factorization, stability of QR factorization.
Module - 3:Solution of linear least squares problems, normal equations, singular value decomposition (SVD), Moore-Penrose inverse, Rank deficient least squares problems, Sensitivity analysis of least-squares problems, Sensitivity of eigenvalues and eigenvectors.
Module - 4: Reduction to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations, Explicit and implicit QR algorithms for symmetric and non-symmetric matrices, Reduction to bi diagonal form, Sensitivity analysis of singular values and singular vectors, conjugate gradient method.
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