β Scribed by A.C. Antoulas
No coin nor oath required. For personal study only.
The problems of approximating linear operators in the 2-induced norm which are (1) finite-dimensional, unstructured, and (2) infinite-dimensional structured (Hankel), have been solved. The solutions of these two problems exhibit striking similarities. These similarities suggest the search of a ur@jingframework for the approximation of linear operators in the 2-induced norm.
π SIMILAR VOLUMES
A theory of best approximation with interpolatory contraints from a finitedimensional subspace M of a normed linear space X is developed. In particular, to each x # X, best approximations are sought from a subset M(x) of M which depends on the element x being approximated. It is shown that this ``pa
Let X, Y be normed linear spaces, T β L(X, Y ) be a bounded linear operator from X to Y . One wants to solve the linear problem Ax = y for x (given y β Y ), as well as one can. When A is invertible, the unique solution is x = A -1 y. If this is not the case, one seeks an approximate solution of the