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- H T Banks, Kathleen Holm, Franz Kappel
- Inverse problems
- 2011

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according… (More)

- Kazufumi Ito, Franz Kappel
- Series on Advances in Mathematics for Applied…
- 2002

Based on the four compartment model by Grodins we develop a model for the response of the cardiovascular system to a short term submaximal workload. Basic mechanisms included in the model are Starling's law of the heart, the Bowditch effect and autoregulation in the peripheral regions. A fundamental assumption is that the action of the feedback control is… (More)

- Franz Kappel, Alexei V. Kuntsevich
- Comp. Opt. and Appl.
- 2000

We consider the problem of estimating a modeling parameter using a weighted least squares criterion (,) = ∑ =1 1 () 2 (() − (,)) 2 for given data by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise (illustrated via examples) being… (More)

- F Kappel, D Salamon
- 1984

The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution… (More)

- Franz Kappel, Martin Fink, Jerry J Batzel
- Mathematical biosciences
- 2007

This paper considers a model developed to study the cardiovascular control system response to orthostatic stress as induced by two variations of lower body negative pressure (LBNP) experiments. This modeling approach has been previously applied to study control responses to transition from rest to aerobic exercise, to transition to non-REM sleep and to… (More)

For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati… (More)

- Kazufumi Ito, Franz Kappel
- Math. Comput.
- 1998

We present formulations of the Trotter-Kato theorem for approximation of linear C 0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation , a wave equation and Stokes' equation as illustrative examples.