Syllabus
1. Basic terminology and relations of the theory of sensitivity and numerical stability.
2. Sensitivity of matrix eigenvalues for general and normal matrices. Continuity and diferentiability, conditioning of a simple eigenvalue. Pseudospectrum.
3. Estimates of backward error for approximations of eigenvalues.
4. Estimates of backward error for approximate solutions of linear algebraic problems.
5. Inverse power method, simultanes subspace iterations.
6. QR algorithm (Francis algorithm) for the solution of full eigenvalue problem and computation of SVD.
7. Summary of related areas and topics.
Annotation
The course extends the curriculum of NMNM331. Recommended for bachelor's program in General Mathematics, specialization Mathematical Modelling and Numerical Analysis.