Bezoutians of rational matrix functions, matrix equations and factorizations

Matrix Functions and Matrix Equations

Solving large-scale algebraic Riccati equations (AREs) is one of the central tasks in solving optimal control problems for linear and, using receding-horizon techniques, also nonlinear instationary partial differential equations. Large-scale AREs also occur in several model reduction methods for dynamical systems. Due to sparsity and large dimensions of the resulting coefficient matrices, stand...

Monotone thematic factorizations of matrix functions

We continue the study of the so-called thematic factorizations of admissible very badly approximable matrix functions. These factorizations were introduced by V.V. Peller and N.J. Young for studying superoptimal approximation by bounded analytic matrix functions. Even though thematic indices associated with a thematic factorization of an admissible very badly approximable matrix function are no...

Rational Methods in Matrix Equations

Riordan group approaches in matrix factorizations

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.

Localization of Matrix Factorizations

Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical algorithms dealing with such matrices often take advantage (implicitly or explicitly) of the empirical observation that this off-diagonal decay property seems to b...