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Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

Heikki Hakkarainen, Juha Kinnunen, Panu Lahti, Pekka Lehtelä (2016)

Analysis and Geometry in Metric Spaces

This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean...

Remarks on inverse of matrix polynomials

Fischer, Cyril, Náprstek, Jiří (2017)

Programs and Algorithms of Numerical Mathematics

Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...

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