Linear System of Equations, Gauss Elimination, Lu and Cholesky Decomposition, Positive Definite Matrices, Least Squares And Pseudo-inverse, Weighted Least-squares, Tikhonov's Regularisation, Inner-products and Normed-vector Spaces, Orthogonality, Qr and Its Uses, Eigenvalues and Singular Values, The Svd Decomposition and Its Uses, Itrative Methods For Solving Linear and Least-squares Problems, Matrix Induced Norms, Gershgorin's Theorem, The Power Method, Numerical Instability and Numerical Erros, Toeplitz and Circulant Matrices, Convolution, The Discrete Fourier Transform and The Fft. Learning Outcomes# By The End of The Course The Studetns Will Be Able To# 1. Use Elementary Decomposition Methods in Numerical Linear Algebra - Lu, Qr, and Svd - According to Their Use and Computational Complexity. 2. Build Algorithms For The Solution of Linear Systems of Equations, Least-squares Problems, and Identification of Eigenvalues And Eigenvectors, By Choosing The Proper Solvers Based On The Properties Of The Problems and Their Dimensions._ 3. Prove Convergence of Iterative Methods For Solving Numerical Problems Via Eigen-analysis, Operators' Norms, and Gershgorin's Disk Theorem. 4. Compute The Discrete Fourier Transform On Vectors, and Diagonalize Circulant Matrices._ 5. Prove Various Advanced Theorems in Linear Algebra Regarding Eigendecomposition of Symmetric, Circulant and Positive Definite Matrices.

Faculty: Computer Science
|Graduate Studies

Pre-required courses

(104016 - Algebra 1/extended and 104166 - Algebra Am)

Parallel course

104032 - Calculus 2m 104281 - Infinitesimal Calculus 2

Course with no extra credit

234125 - Numerical Algorithms

Course with no extra credit (contained)

104283 - Introduction to Numerical Analysis 234107 - Numerical Analysis 1

Course with no extra credit (contains)

34033 - Numerical Analysis M 34056 - Int. to Scientific and Eng. Computing 84135 - Numerical Analysis For Aerospace Engi. 95295 - Algebraic Methods For Data Science

Semestrial Information