The spectral abscissa is a fundamental map from the set of complex matrices to the real numbers. Denoted α and defined as the maximum of the real parts of the eigenvalues of a matrix X, it has many applications in st...
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We propose a new implementation of the sign function based spectral divide-and-conquer method for the generalized non-symmetric eigenvalue problem. The basic idea is to use the generalized matrix sign function to spli...
Linear time-periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Stability of the solution may be proven by rigorous bounds on the solution. The key idea of this paper is to de...
The M.E.S.S. software suite for solving large scale matrix equations and related problems is the successor of the obsolete LyaPack MATLAB® toolbox. The software suite consists of a new MATLAB toolbox and a separa...
We investigate the application of the LR Cholesky algorithm to symmetric hierarchical matrices, symmetric simple structured hierarchical matrices and symmetric hierarchically semiseparable (HSS) matrices. The data-spa...
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In this paper, we develop an approach to achieve either frequency or amplitude modulation of an oscillator merely through feedback control. We present and implement a unified theory of our approach for any finite-dime...
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In this paper, we develop an approach to achieve either frequency or amplitude modulation of an oscillator merely through feedback control. We present and implement a unified theory of our approach for any finite-dimensional continuous dynamical system that exhibits oscillatory behavior. The approach is illustrated not only for the normal forms of dynamical systems but also for representative biological models, such as the isolated and coupled FitzHugh-Nagumo model. We demonstrate the potential usefulness of our approach to uncover the mechanisms of frequency and amplitude modulations experimentally observed in a wide range of real systems.
Efficient numerical algorithms for the solution of large and sparse matrix Riccati and Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have become available around the year 200...
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Descriptor Lur’e equations are an important tool for the solution of linear-quadratic optimal control problems for differential-algebraic systems. In this article we discuss how one can construct all solutions of the...
We discuss the infinite time-horizon linear-quadratic optimal control problem for differential-algebraic equations. In contrast to previous approaches we do not impose any assumptions on the system except for impulse ...
This paper describes a model order reduction technique for circuit simulation, based on the parallelization of the well-known multi-point PRIMA algorithm. In order to obtain an optimal accuracy of the reduced-order mo...
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This paper describes a model order reduction technique for circuit simulation, based on the parallelization of the well-known multi-point PRIMA algorithm. In order to obtain an optimal accuracy of the reduced-order model in the entire frequency range of interest, the reduced models are computed on different expansion points in correspondence of which the errors, between the transfer functions of the original model and of the actual reduced one, exhibit the largest value, in a recursive way. Moreover, since the computation of the error is a computationally expensive routine, this task is parallelized, assuming that each error value is independent of the others and to work with modern multi-core computers or a cluster of workstations. The numerical results show that the parallelized model order reduction algorithm is able to provide accuracy and speed up with respect to the sequential one, for both dense and sparse data sets.
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