Week 1: Introduction to matrix and equation systems (1) Symmetric matrix and transpose (1) Determinant and rank(1) , Gauss elimination(2), Row permutation (1)
Week 2: Inverse of Matrix (1), Gauss Jordon Method for Finding Inverse(2) Matrix form of difference equations (1) Tridiagonal matrix algorithm (2)
Week 3: Introduction to vector space (1) Column space and row space (1) Null space from solving Ax=0(3) Solving Ax=b (1)
Week 4: Linear independence and spanning (1) Basis and dimension (1) Four fundamental subspaces and solvability of a matrix equation (2) Linear transformation (2)
Week 5: Gram-Schmidt orthogonalization(3) QR Factorization for Normal equation (1) Eigen values, eigen vectors, spectral radius (2)
Week 6: Mid term exam
Week 7: Introduction to iterative methods, Gauss-Siedel, Jacobi and SOR (4) Convergence of iterative methods (2)
Week 8: Introduction to programming of matrix algorithms and code demonstration (2) Steepest descent algorithm and its variants (4)
Week 9: Introduction to Krylov subspaces(2) Krylov subspace for Av, Arnoldi’’s Algorithm (2) GMRES (2)
Week 10: Lanczos method for symmetric matrix (1) Conjugate gradient method (1) Krylov subspace for ATv, biorthogonalization and Biconjugate gradient and BiCG-STAB(4)
Week 11: Lanczos method for symmetric matrix (1) Conjugate gradient method (1) Krylov subspace for ATv, biorthogonalization and Biconjugate gradient and BiCG-STAB(4)
Week 12: Block relaxation schemes (2) Introduction to Preconditioner and Multigrid Methods (4)
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