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
a.Iterative solution of non-linear systems of algebraic equations. Contraction principle = functional iteration.
b. Roots of a function. Newton's method.