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Approximation. --- Dimensional analysis. --- Feedback control. --- Linearity. --- Quadratic equations.

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This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.

Algorithms. --- Mathematics. --- Matrices. --- Vector algebra. --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Equations, Quadratic. --- Algebra, Vector --- Algorism --- Quadratic equations --- Algebra. --- Algebras, Linear --- Vector analysis --- Arithmetic --- Foundations --- Mathematical analysis

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Group theory --- 51 <082.1> --- Mathematics--Series --- Geometric group theory --- Statistical decision --- Free products (Group theory) --- Equations, Quadratic --- Groupes, Théorie géométrique des --- Prise de décision (statistique) --- Équations du second degré --- Decision problems --- Game theory --- Operations research --- Statistics --- Management science --- Products, Free (Group theory) --- Quadratic equations --- Groupes, Théorie géométrique des. --- Équations du second degré.

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Artificial intelligence --- Computer-assisted instruction --- Equations, Quadratic --- Ordinateurs Computers --- Programmes de formation Opleidingsprogramma's --- Autodidactes Zelfstudie --- Stratégies (formation) Opleidingsstrategieën --- Politique de formation Opleidingsbeleid --- Enseignement programmé Geprogrammeerd onderwijs --- Quadratic equations --- CAI (Computer-assisted instruction) --- Computer-aided instruction --- Computer-assisted learning --- Computer based instruction --- Computer-enhanced learning --- Electronic data processing in programmed instruction --- ILSs (Integrated learning systems) --- Integrated learning systems --- Microcomputer-aided instruction --- Microcomputer-assisted instruction --- Microcomputer-assisted learning --- Microcomputer-based instruction --- Teaching --- Education --- Educational technology --- Programmed instruction --- Telematics --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Data processing --- Artificial intelligence. --- Self Improving Teaching --- Cai

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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Mathematical notation --- History. --- Abu Jafar Muhammad ibn Musa al-Khwārizmī. --- Alexandria. --- Arabic alphabet. --- Arabic numbers. --- Arabs. --- Arithmetica Integra. --- Arithmetica. --- Ars Magna. --- Aztec numerals. --- Babylonians. --- Brahmagupta. --- Brahmasphutasiddhanta. --- Brahmi number system. --- Cartesian coordinate system. --- China. --- Chinese. --- Christoff Rudolff. --- Clavis mathematicae. --- Die Coss. --- Diophantus. --- Egyptian hieroglyphics. --- Elements. --- Euclid. --- Eurasia. --- Europe. --- France. --- François Viète. --- Geometria. --- George Rusby Kaye. --- Gerbertian abacus. --- Gerolamo Cardano. --- Gottfried Leibniz. --- Gotthilf von Schubert. --- Greek alphabet. --- Heron of Alexandria. --- Hindu-Arabic numerals. --- Ibn al-Qifti. --- India. --- Indian mathematics. --- Indian numbers. --- Indian numerals. --- Invisible Gorilla experiment. --- Isaac Newton. --- Jacques Hadamard. --- Kanka. --- L'Algebra. --- Leonardo Fibonacci. --- Liber abbaci. --- Ludwig Wittgenstein. --- Mayan system. --- Metrica. --- Michael Stifel. --- Michel Chasles. --- Nicolas Chuquet. --- Proclus. --- Pythagorean theorem. --- Rafael Bombelli. --- René Descartes. --- Roman numerals. --- Royal Road. --- Sanskrit. --- Silk Road. --- St. Andrews cross. --- Stanislas Dehaene. --- Ta'rikh al-hukama. --- William Jones. --- William Oughtred. --- abacus. --- al-Qalasādi. --- algebra. --- algebraic expressions. --- algebraic symbols. --- alphabet. --- ancient number system. --- arithmetic. --- calculus. --- counting rods. --- counting. --- curves. --- decimal system. --- dependent variables. --- dignità. --- dreams. --- dust boards. --- equality. --- equations. --- exponents. --- finger counting. --- fluents. --- fluxions. --- forgeries. --- geometry. --- homogeneous equations. --- images. --- infinitesimals. --- juxtaposition. --- known quantities. --- language. --- mathematical notation. --- mathematics. --- meaning. --- mental pictures. --- metaphor. --- modern arithmetic. --- modern number system. --- multiplication. --- natural language. --- negative numbers. --- nested square roots. --- notation. --- number system. --- numbers. --- numerals. --- operations. --- place-value. --- poetry. --- polynomials. --- positive numbers. --- powers. --- prime numbers. --- proofs. --- quadratic equations. --- reckoning. --- sexagesimal system. --- square roots. --- symbolic algebra. --- symbols. --- thought. --- trade. --- verbal language. --- vinculum. --- vowel--consonant notation. --- words. --- writing.