Learn More
Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomial (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations that reflect the structure of these polynomials, and therefore(More)
of Berlin. In collaboration with the company SFE they study the resonances when rail tracks are excited by high speed trains, the goal being to reduce noise and vibrations in the trains. The new ICE trains travel across Europe at speeds as high as 300 km/h but the numerical methods used to design them are at least 30 years old. More often than not the(More)
We present structure-preserving numerical methods for the eigenvalue problem of complex palindromic pencils. Such problems arise in control theory, as well as from palindromic linearizations of higher degree palindromic matrix polynomials. A key ingredient of these methods is the development of an appropriate condensed form — the anti-triangular Schur form.(More)
In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils λS − H, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur for example in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving(More)
It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant sub-space always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative(More)
The polar decomposition of a square matrix has been generalized by several authors to scalar products on R n or C n given by a bilinear or sesquilinear form. Previous work has focused mainly on the case of square matrices, sometimes with the assumption of a Hermitian scalar product. We introduce the canonical generalized polar decomposition A = W S, defined(More)
OBJECTIVES The purpose of this in vitro study was to evaluate the wear of six composite resins for the veneering of crowns compared with the wear of human and bovine enamel, tested in a dual-axis chewing simulator. METHODS Eight specimens of six different composite resins (Targis I+II, Solidex, BelleglassHP, Estenia, Solidex) and of human and bovine(More)
Eucommia ulmoides Oliv. (EuO), also known as Duzhong, native to China, has been reported to have antioxidative function, but its cellular mechanism is not fully examined yet. We investigated inhibitory effects of EuO leaf ethanol extracts on H(2)O(2)-induced apoptosis in rat osteoblastic MC3T3-E1 cells and underlying mechanisms. Locally-grown Duzhong leaves(More)
We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the(More)