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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Nonlinear systems --- Mathematical models. --- Systems, Nonlinear --- System theory --- Calculus of variations. --- Eigenvalues. --- Calculus of variations --- Eigenvalues

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The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.

Differential equations, Partial. --- Eigenvalues. --- Geometry, Riemannian. --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Matrices --- Partial differential equations --- Differential equations, Partial --- Eigenvalues --- Geometry, Riemannian --- Equations aux dérivées partielles --- Valeurs propres --- Riemann, Géométrie de

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Matrix Singular Value Decomposition (SVD) and its application to problems in signal processing is explored in this book. The papers discuss algorithms and implementation architectures for computing the SVD, as well as a variety of applications such as systems and signal modeling and detection. The publication presents a number of keynote papers, highlighting recent developments in the field, namely large scale SVD applications, isospectral matrix flows, Riemannian SVD and consistent signal reconstruction. It also features a translation of a historical paper by Eugenio Beltrami, containing on

Signal processing --- Decomposition (Mathematics) --- Digital techniques --- Congresses --- -Signal processing --- -Academic collection --- #TELE:SISTA --- 519.6 --- 681.3*G13 --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Mathematics --- Probabilities --- -Congresses --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Academic collection --- Digital techniques&delete& --- Decomposition (Mathematics) - Congresses. --- Signal processing - Digital techniques - Congresses --- Decomposition (Mathematics) - Congresses --- Signals --- Processing

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Sparse matrices

Numerical analysis --- Sparse matrices. --- Matrices éparses. --- Analyse numérique. --- Algèbre linéaire. --- Algebras, Linear --- Matrices --- Algebra, Universal. --- Data processing. --- Data processing --- 519.6 --- 681.3*G13 --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Algebra, Multiple --- Multiple algebra --- N-way algebra --- Universal algebra --- Algebra, Abstract --- Numbers, Complex --- Analyse numérique --- Algèbre linéaire --- Numerical analysis. --- Algebras, Linear. --- Matrices - Data processing --- Calcul matriciel --- Methodes numeriques

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This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.

Physical Sciences & Mathematics --- Sciences - General --- Chaotic behavior in systems --- Time-series analysis --- Mathematical models. --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- reliability --- psychological tests --- psychometrics --- human being --- classification --- case study --- Attractor --- Eigenvalues and eigenvectors --- Markov chain --- Stationary process --- Time series