One major area in the theory of statistical signal processing is
reduced-rank - timation where optimal linear estimators are approximated
in low-dimensional subspaces, e.g., in order to reduce the noise in
overmodeled problems, - hance the performance in case of estimated
statistics, and/or save compu- tional complexity in the design of the
estimator which requires the solution of linear equation systems. This
book provides a comprehensive overview over reduced-rank ?lters where
the main emphasis is put on matrix-valued ?lters whose design requires
the solution of linear systems with multiple right-hand sides. In
particular, the multistage matrix Wiener ?lter, i.e., a reduced-rank
Wiener ?lter based on the multistage decomposition, is derived in its
most general form. In numerical mathematics, iterative block Krylov
methods are very po- lar techniques for solving systems of linear
equations with multiple right-hand sides, especially if the systems are
large and sparse. Besides presenting a - tailed overview of the most
important block Krylov methods in Chapter 3, which may also serve as an
introduction to the topic, their connection to the multistage matrix
Wiener ?lter is revealed in this book. Especially, the reader will learn
the restrictions of the multistage matrix Wiener ?lter which are
necessary in order to end up in a block Krylov method. This relationship
is of great theoretical importance because it connects two di?erent
?elds of mathematics, viz., statistical signal processing and numerical
linear algebra.
