Numerical Algebra & Analysis

0. Numerics -preliminaries:  floating point representation of numbers, numerical stability, condition number

1.Numerical linear algebra

       a.Matrices, vectors, specialized matrices (orthogonal, symmetric), eigen-values, eigen-vectors, determinant, inverse, rank, trace, norms

        b. Matrix decompositions and algorithms: QR (Gram-Schmidt, Householder, Cholesky), LU (Gaussian elimination, pivoting), Singular Value Decomposition

2.Numerical analysis

       a.Iterative solution of non-linear systems of algebraic equations. Contraction principle = functional iteration.

        b.  Roots of a function. Newton's method.