Syllabus
The course will cover primarily projection methods and, in particular, Krylov subspace methods in relation to the problem of moments and related issues. The emphasis will be on interconnections between the relevant topics from various disciplines, including the elements of numerical solution of partial differential equations, approximation theory and functional analysis. Tentative content:
1. Projection processes
2. Krylov subspaces
3. Basic methods
4. Stieltjes moment problem
5. Orthogonal polynomials, continued fractions, Gauss-Christoffel quadrature and model reduction
6. Matrix representation and the method of conjugate gradients
7. Vorobyev method of moments and non-symmetric generalizations
8. Non-normality and spectral information
Annotation
The course will deal with the general theory of projective methods, in particular, Krylov subspace methods and their relation to the problem of moments.