TOPICS IN NUMERICAL ANALYSIS & APPLIED MATHEMATICS

Description.

Norms for vectors and matrices. Characteristic and minimal polynomial of a matrix. Properties eigenvalues and eigenvectors of the special matrices (symmetric, Hermitian, normal, unitary, orthogonal). Schur’s triangularization theorem. Canonical forms (diagonalization, Jordan canonical form). Singular value Decomposition (SVD) and its applications. Factorization QR, LU, and the associated algorithms. Positive matrices. Nonnegative matrices. Irredusible nonnegative matrices, Primitive matrices. Numerical range of a matrix and its properties. Matrix polynomials and their applications on differential equations. Interpolation (linear, cubic, Lagrange, Spline, Hermite). Interpolation kernels. Applications. Numerical solutions of Partial Differential Equations and their applications on image processing. Numerical integration.

Bibliography:
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21. https://hal.inria.fr/hal-01459628