Jaroslav Kautsky

Bio: Jaroslav Kautsky is an academic researcher from Flinders University. The author has contributed to research in topics: Orthogonal polynomials & Matrix (mathematics). The author has an hindex of 19, co-authored 48 publications receiving 2273 citations.

Jacobi m atrices f or s ums o f w eight f unctions

Abstract: Orthogonal polynomials are conveniently represented by the tridiagonal Jacobi matrix of coefficients of the recurrence relation which they satisfy. Let J1 and J2 be finite Jacobi matrices for the weight functions wl and w2, resp. Is it possible to determine a Jacobi matrix i, corresponding to the weight functions ff = w~ + w2 using only J~ and J2 and if so, what can be said about its dimension? Thus, it is important to clarify the connection between a finite Jacobi matrix and its corresponding weight function(s). This leads to the need for stable numerical processes that evaluate such matrices. Three new O(n z) methods are derived that "merge" Jacobi matrices directly without using any information about the corresponding weight functions. The first can be implemented using any of the updating techniques developed earlier by the authors. The second new method, based on rotations, is the most stable. The third new method is closely related to the modified Chebyshev algorithm and, although it is the most economical of the three, suffers from instability for certain kinds of data. The concepts and the methods are illustrated by small numerical examples, the algorithms are outlined and the results of numerical tests are reported.

Discrete biorthogonal wavelets and PR finite impulse response (FIR) filter banks via block circulant matrices

Abstract: Factorization of orthogonal block circulant matrices can not be generalized in a straightforward way for block circulant matrices which are merely invertible. However, they can be decomposed into an orthogonal matrix and an atom that represents the `nonorthogonal' part of the matrix. Atoms can be characterized by nilpotent block-companion matrices. This characterization permits, for example, to derive bounds for the width of the band of the inverse of a banded block circulant matrix.

Robust Model-Based Fault Diagnosis for Dynamic Systems

Abstract: There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Introduction to Wavelets and Wavelet Transforms: A Primer

Abstract: 1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

The Quadratic Eigenvalue Problem

Abstract: We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

Robust pole assignment in linear state feedback

Abstract: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.