for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of L∞ in L (R,C ), 1 < p < ∞, is the following L-dissipativity condition...

a companion of ostrowski's inequality for functions of bounded variation and applications are given.

A companion of Ostrowski's inequality for functions of bounded variation and applications are given.

This paper is concerned with the reduction of a unitary matrix U to CMV-like shape. A Lanczos–type algorithm is presented which carries out the reduction by computing the block tridiagonal form of the Hermitian part of U , i.e., of the matrix U +UH . By elaborating on the Lanczos approach we also propose an alternative algorithm using elementary matrices which is numerically stable. If U is ran...

In this paper, solutions to the generalized Sylvester matrix equations AX−XF = BY and MXN−X = TY with A, M ∈ Rn×n, B, T ∈ Rn×r, F, N ∈ Rp×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × (n + pr). The algorithm proposed in this paper for the euqation AX − XF = BY does not require the controllability of matrix pair...

A standard way to solve polynomial eigenvalue problems P (λ)x = 0 is to convert the matrix polynomial P (λ) into a matrix pencil that preserves its elementary divisors and, therefore, its eigenvalues. This process is known as linearization and is not unique, since there are infinitely many linearizations with widely varying properties associated with P (λ). This freedom has motivated the recent...