Review: Numerical Treatment o f Eigenvalue Problems, Vol. 5. (Workshop in Oberwolfach, February 25 - March 3. 1990), Edited by: J. Albrecht, L. Collatz, P. Hagedorn, W. Veite
The article contains no abstract
Some remarks on spectral approximation for compact operators
Finite-dimensional approximations for linear compact operators are constructed by discretization of the underlying Banach space. Sufficient conditions for strong convergence of the finite-dimensional operators to the given compact operator and for their collective compactness are obtained. In particular, the finite-dimensional approximation of the pencil A−λJ:H→V is considered, where H,V are Banach spaces, A is an invertible and J a compact operator.
Semiiterative methods for linear equations
The authors consider the numerical solution of Ax=f, where A is a bounded invertible linear operator in a complex Banach space, (i) using only premultiplication of vectors by A and (ii) forming linear combinations of known vectors. Essentially, this involves the approximation of A^(−1) by polynomials in A. Several methods of computing this approximation are investigated.
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