Hyperbolic rotation of subspaces and VLSI algorithms for signal processing and numerical linear algebra

Starting from the viewpoint of linear physical systems, a brief study is presented of energy-conserving or J-orthogonal transformations in a space with an indefinite metric under the special aspect of their VLSI realization. A mesh-connected array of n ² processor cells, each performing a plane hyperbolic rotation, is shown to be the most natural of n-dimensional subspaces. Isometric linear fractional maps of contractive matrices to the zero matrix and hyperbolic Cholesky factorization are presented as the most interesting applications in generalized Schur methods, digital signal processing, and numerical linear algebra. Using the Cholesky factorization as an example, a square-root- and division-free computation scheme for hyperbolic rotations that is highly suited for VLSI implementation is presented