Patrick Dewilde

Bio: Patrick Dewilde is an academic researcher from Delft University of Technology. The author has contributed to research in topics: Matrix (mathematics) & Triangular matrix. The author has an hindex of 19, co-authored 66 publications receiving 2125 citations. Previous affiliations of Patrick Dewilde include Technische Universität München.

Subspace model identification Part 1. The output-error state-space model identification class of algorithms

Abstract: In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

A Fast Solver for HSS Representations via Sparse Matrices

Abstract: In this paper we present a fast direct solver for certain classes of dense structured linear systems that works by first converting the given dense system to a larger system of block sparse equations and then uses standard sparse direct solvers. The kind of matrix structures that we consider are induced by numerical low rank in the off-diagonal blocks of the matrix and are related to the structures exploited by the fast multipole method (FMM) of Greengard and Rokhlin. The special structure that we exploit in this paper is captured by what we term the hierarchically semiseparable (HSS) representation of a matrix. Numerical experiments indicate that the method is probably backward stable.

Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences

Abstract: An exact and approximate realization theory for estimation and model filters of second-order stationary stochastic sequences is presented. The properties of J -lossless matrices as a unifying framework are used. Necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a J -lossless system are deduced. An extension of the so-called Schur algorithm yields an approximate J -lossless realization based on partial past information about the process. The geometric properties of such partial realizations and their convergence are studied. Finally, connections with the Nevanlinna-Pick problem are made, and how the techniques presented constitute a generalization of many aspects of the Levinson-Szego theory of partial realizations is shown. As a consequence generalized recursive formulas for reproducing kernels and Christoffel-Darboux formulas are obtained. In this paper the scalar case is considered. The matrix case will be considered in a separate publication.

Lossless chain scattering matrices and optimum linear prediction: The vector case

Abstract: In this paper we give a systematic treatment of the exact and approximate realization of a positive real matrix-valued function on the open unit disc by means of a lossless circuit connected to a passive load. We discuss the mathematical properties of the chain scattering matrix which describes the lossless circuit and rederive a form of the classical Darlington synthesis theorem generalized to roomy matrix-valued transmission functions. We then develop a matrix version of an algorithm due to Schur for the construction of approximate realizations which produces (minimal degree) Nevanlinna–Pick approximants to the original positive real matrix. We further identify the normalized inverse of one of the outer factors of the approximant to the positive real matrix as the orthogonal projection of the identity onto a suitably defined subspace, give its interpretation as a reproducing kernel, and establish strong convergence under mild conditions on the growth of the order of the approximation. Finally we interpret and apply the mathematical theory developed in the body of the paper to the theory of prediction for vector-valued second order stationary stochastic sequences and briefly discuss connections with the theory of maximum entropy extensions and of inverse scattering.

Linear systems

Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

Stochastic systems : estimation, identification, and adaptive control

Abstract: stochastic systems estimation identification and adaptive stochastic adaptive control eolss stochastic systems estimation identification and adaptive stochastic systems estimation identification and adaptive control of stochastic systems eolss stochastic systems estimation identification and adaptive stochastic systems: estimation, identification and adaptation in stochastic dynamic systems survey and new identification and stochastic adaptive control (systems identification and adaptive control methods for some robust stochastic adaptive control dspace@mit: home adaptation in stochastic dynamic systems survey and new chapter 1: introduction to adaptive control stochastic systems estimation identification and adaptive stochastic adaptive nash certainty equivalence control coefficient estimation in adaptive control systems maximum likelihood identification and realization of (size 44,85mb) download ebook stable adaptive systems optimal adaptive control of uncertain stochastic discrete 19,42mb file download system identification adaptive on-line identification and adaptive trajectory tracking ece686: filtering and control of stochastic linear systems robustness and convergence of least-squares identification 68,58mb file system identification adaptive control bahram adaptation in stochastic dynamic systems survey and new identification and system parameter estimation 1991 gbv stochastic adaptive control via consistent parameter adaptive control of stochastic sage pub stochastic delay estimation and adaptive control of eece 574 adaptive control basics of system identification robust identification of stochastic linear systems with robust adaptive els-qr algorithm for linear discrete time stochastic systems: the mathematics of filtering and ee/ise 556: stochastic systems fall 2013 usc search identification and system parameter estimation 1991 gbv

Wave digital filters: Theory and practice

Abstract: Wave digital filters (WDFs) are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof. They have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions. A detailed review of WDF theory is given. For this several goals are set: to offer an introduction for those not familiar with the subject, to stress practical aspects in order to serve as a guide for those wanting to design or apply WDFs, and to give insight into the broad range of aspects of WDF theory and its many relationships with other areas, especially in the signal-processing field. Correspondingly, mathematical analyses are included only if necessary for gaining essential insight, while for all details of more special nature reference is made to existing literature.

FastCap: a multipole accelerated 3-D capacitance extraction program

Abstract: A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy. >