Results 1  10
of
85
Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods
, 2004
"... We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the JacobiDavidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new li ..."
Abstract

Cited by 42 (4 self)
 Add to MetaCart
(Show Context)
We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the JacobiDavidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods. We present several recent applications where structured and unstructured nonlinear eigenvalue problems arise and some numerical results.
Modelica  a language for physical system modeling, visualization and interaction
 In 1999 IEEE Symposium on ComputerAided Control System Design
, 1999
"... Modelica is an objectoriented language for modeling of large, complex and heterogeneous physical systems. It is suited for multidomain modeling, for example for modeling of mechatronics including cars, aircrafts and industrial robots which typically consist of mechanical, electrical and hydraulic ..."
Abstract

Cited by 38 (3 self)
 Add to MetaCart
Modelica is an objectoriented language for modeling of large, complex and heterogeneous physical systems. It is suited for multidomain modeling, for example for modeling of mechatronics including cars, aircrafts and industrial robots which typically consist of mechanical, electrical and hydraulic subsystems as well as control systems. General equations are used for modeling of the physical phenomena. No particular variable needs to be solved for manually. A Modelica tool will have enough information to do that automatically. The language has been designed to allow tools to generate efficient code automatically. The modeling effort is thus reduced considerably since model components can be reused and tedious and errorprone manual manipulations are not needed. The principles of objectoriented modeling and the details of the Modelica language as well as several examples are presented. 1.
A DESCRIPTOR SYSTEMS Toolbox for MATLAB
 Proc. of CACSD’2000 Symposium
"... Abstract: The recently developed PERIODIC SYSTEMS Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via exible and functionally rich high level mfunctions, while simultaneously enforcing highly efcient an ..."
Abstract

Cited by 27 (14 self)
 Add to MetaCart
Abstract: The recently developed PERIODIC SYSTEMS Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via exible and functionally rich high level mfunctions, while simultaneously enforcing highly efcient and numerically sound computations via the mexfunction technology of MATLAB to solve critical numerical problems. The mfunctions based user interfaces ensure userfriendliness in operating with the functions of this toolbox via an object oriented approach to handle periodic system descriptions. The mexfunctions are based on FORTRAN implementations of recently developed structure exploiting and structure preserving numerical algorithms for periodic systems which completely avoid forming of lifted representations. Copyright c
2005 IFAC
Minimal statespace realization in linear system theory: An overview
 JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, 2000
"... ..."
(Show Context)
BlockToeplitz/Hankel Structured Total Least Squares
, 2003
"... Abstract. A structured total least squares problem is considered in which the extended data matrix is partitioned into blocks and each of the blocks is blockToeplitz/Hankel structured, unstructured, or exact. An equivalent optimization problem is derived and its properties are established. The spe ..."
Abstract

Cited by 24 (17 self)
 Add to MetaCart
(Show Context)
Abstract. A structured total least squares problem is considered in which the extended data matrix is partitioned into blocks and each of the blocks is blockToeplitz/Hankel structured, unstructured, or exact. An equivalent optimization problem is derived and its properties are established. The special structure of the equivalent problem enables us to improve the computational efficiency of the numerical solution methods. By exploiting the structure, the computational complexity of the algorithms (local optimization methods) per iteration is linear in the sample size. Application of the method for system identification and for model reduction is illustrated by simulation examples.
Mechanical Derivation and Systematic Analysis of Correct Linear Algebra Algorithms
, 2006
"... We consider the problem of developing formally correct dense linear algebra libraries. The problem would be solved convincingly if, starting from the mathematical speciﬁcation of a target operation, it were possible to generate, implement and analyze a family of correct algorithms that compute the o ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
We consider the problem of developing formally correct dense linear algebra libraries. The problem would be solved convincingly if, starting from the mathematical speciﬁcation of a target operation, it were possible to generate, implement and analyze a family of correct algorithms that compute the operation. This thesis presents evidence that for a class of dense linear operations, systematic and mechanical development of algorithms is within reach. It describes and demonstrates an approach for deriving and implementing, systematically and even mechanically, proven correct algorithms. It also introduces a systematic procedure to analyze, in a modular fashion, numerical properties of the generated algorithms.
Application of Structured Total Least Squares for System Identification and Model Reduction
 IEEE TRANS. AUTOMAT. CONTROL
, 2004
"... ..."
Computation of General InnerOuter and Spectral Factorizations
 IEEE TRANS. AUTO. CONTR
, 2000
"... In this paper we solve two problems in linear systems theory: the computation of the innerouter and spectral factorizations of a continuoustime system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a stan ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
In this paper we solve two problems in linear systems theory: the computation of the innerouter and spectral factorizations of a continuoustime system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the transfer function matrix of the system. The proposed procedures are completely general being applicable for a polynomial /proper/improper system whose transfer function matrix could be rank deficient and could have poles/zeros on the imaginary axis or at infinity. As an application we discuss the extension to rational matrices of the complete orthogonal decomposition of a constant matrix. Numerical refinements are discussed in detail. To illustrate the proposed approach several numerical examples are also given.
The sensitivity of computational control problems
 IEEE Control Syst. Mag
, 2004
"... What factors contribute to the accurate and efficient numerical solution of problems in control systems analysis and design? Although numerical methods have been used for many centuries to solve problems in science and engineering, the importance of computation grew tremendously with the advent of d ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
What factors contribute to the accurate and efficient numerical solution of problems in control systems analysis and design? Although numerical methods have been used for many centuries to solve problems in science and engineering, the importance of computation grew tremendously with the advent of digital computers. It became immediately clear that many of the classical analytical and numerical methods and algorithms could not be implemented directly as computer codes, although they were well suited for hand computations. What was the reason? When doing computations by hand a person can choose the accuracy of each elementary calculation and then estimate, based on intuition and experience, its influence on the final result. In contrast, when computations are done automatically, intuitive error control is usually not possible and the effect of errors on the intermediate calculations must be estimated in a more systematic way. Due to this observation, starting