A Parallel Computer Architecture Oriented Towards the Eigenvalue-Eigenvector Representation of Operators

Summary

Compact normal operators on Hilbert spaces are regarded, they are resolvable in weighted sums of projections. This implies that - once given the spectral coefficients - the “operator” simply reduces to a number of multiplications of the spectral coefficients by the corresponding eigenvalues. A parallel computer system is presented consisting of system elements of a digital differential analyzer. They are best suited because they are capable of performing those basic operations asked for when resolving operators in weihted sums of projections: the Stieltjes integration and the constant- multiplication. The interconnection structure of the system elements is the same fixed one for all the different operators of the compact normal type. The peculiarity of a definite operator is simply pinpointed by means of information, i.e. the eigenvectors and eigenvalues. This makes the parallel computer system an easily applicable tool for simulation purposes.