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Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines.

Algorithms --- Matrius disperses --- Sistemes lineals --- Algorismes

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This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar’s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker’s sampling theorem for band-limited functions, and Shannon’s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis.

Algebra --- Mathematics --- Electrical engineering --- algebra --- automatisering --- systeemtheorie --- wiskunde --- automatische regeltechniek --- Automatic control. --- Automatic control --- Sistemes lineals --- Data processing.

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Control theory. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Dynamics --- Machine theory --- Philosophy --- Teoria de control --- Teoria de sistemes --- Filosofia de la ciència --- Anàlisi de sistemes --- Autopoesi --- Caos (Teoria de sistemes) --- Enginyeria de sistemes --- Sistemes biològics --- Sistemes complexos --- Sistemes lineals --- Sistemes no lineals --- Sistemes socials --- Control (Matemàtica) --- Control òptim --- Regulació --- Teoria de màquines --- Control automàtic --- Filtre de Kalman --- Sistemes de control biològic

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Teoria de sistemes --- Dinàmica --- Cinètica --- Matemàtica --- Mecànica analítica --- Aerodinàmica --- Cinemàtica --- Caos (Teoria de sistemes) --- Dinàmica molecular --- Electrodinàmica --- Estabilitat --- Matèria --- Moviment --- Moviment rotatori --- Pertorbació (Matemàtica) --- Teoria quàntica --- Termodinàmica --- Estàtica --- Física --- Energia --- Mecànica --- Filosofia de la ciència --- Anàlisi de sistemes --- Autopoesi --- Enginyeria de sistemes --- Sistemes biològics --- Sistemes complexos --- Sistemes lineals --- Sistemes no lineals --- Sistemes socials --- System theory --- Dynamics --- History. --- Statistical methods. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Systems, Theory of --- Systems science --- Science --- Philosophy

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Critical realism. --- System theory. --- Teachers --- Training of --- Philosophy. --- Faculty (Education) --- Instructors --- School teachers --- Schoolteachers --- School employees --- Systems, Theory of --- Systems science --- Science --- Philosophy, Modern --- Realism --- Philosophy --- Formació del professorat --- Filosofia de l'educació --- Teoria de sistemes --- Filosofia de la ciència --- Anàlisi de sistemes --- Autopoesi --- Caos (Teoria de sistemes) --- Enginyeria de sistemes --- Sistemes biològics --- Sistemes complexos --- Sistemes lineals --- Sistemes no lineals --- Sistemes socials --- Filosofia social --- Antropologia educativa --- Teoria de l'educació --- Formació d'educadors --- Formació dels mestres --- Perfeccionament del professorat --- Formació --- Escoles normals --- Observació (Mètode d'ensenyament) --- Pràctiques pedagògiques --- Professors