Syllabus
1. Introduction. What is numerical mathematics.
2. Problem types and errors (forward, backward, residual). Distinguishing factorization and eigenvalue problems.
3. Schur theorem and its consequences.
4. Orthogonality. QR factorization. Time complexity of the QR factorization and its stability.
5. LU factorization and solving systems of linear equations. Growth of errors in solving systems of linear equations.
6. Singular value decomposition. Least-squares problems.
7. Iterative methods based on splittings. Power method for eigenvalue problems. Ideas behind Krylov space methods.
Annotation
The first course of numerical linear algebra for students of MMIB.