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The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.

The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.

The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

Lineaire vergelijkingen. --- Projectiemethoden (wiskunde) --- Equations, Simultaneous --- Iterative methods (Mathematics) --- Itération (Mathématiques) --- Numerical solutions. --- -Iterative methods (Mathematics) --- #TELE:SISTA --- 519.6 --- 681.3*G13 --- Iteration (Mathematics) --- Numerical analysis --- Simultaneous equations --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 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 --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Equations, Simultaneous - Numerical solutions.

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Outside the professional circles of topography and applied mathematics, the life and work of André-Louis Cholesky (1875–1918) are still relatively unknown to the scientific community. This new book appreciably widens the exposure of his remarkable personal achievements in topography and mathematics to a much larger international audience. Cholesky is also interesting to historians because he is a perfect representative of the "scientists engineers" that, since the early 19th century, had issued from the French scientific high schools. Because they had received a high level of mathematical education, they were able to innovate in their practice of engineering. In the case of Cholesky, this resulted in original contributions in artillery, topography, numerical analysis and graphical calculation. In addition, the book places his education and works within the history of several European countries through the 17th to 19th centuries. The book begins with Cholesky's biography, followed by his family’s history and an introduction to topography. It continues with a historical analysis of an unpublished paper (translated into English) in which Cholesky explained his method for linear systems. Cholesky's other works are then described, such as his participation in teaching at a superior "school by correspondence" founded by Léon Eyrolles. His important unpublished book in French on graphical calculation, which is reproduced in its entirety, is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper on Cholesky's method, is provided. Various documents, highlighting the life and the personality of Cholesky, round out his story and end the book.

Mathematics --- Mathematicians --- Armies --- History. --- Officers --- Army --- Military power --- Armed Forces --- Math --- Science --- Mathematics. --- Computer science --- History of Mathematical Sciences. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Annals --- Auxiliary sciences of history

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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area.   This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.   Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation   Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature   Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi.

Numerical integration. --- Orthogonal polynomials. --- Gautschi, Walter. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Mathematics. --- Computer science --- Approximation theory. --- Differential equations. --- Numerical analysis. --- History. --- Numerical Analysis. --- Mathematics of Computing. --- Approximations and Expansions. --- History of Mathematical Sciences. --- Ordinary Differential Equations. --- Definite integrals --- Interpolation --- Numerical analysis --- Computer science. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Informatics --- Mathematical analysis --- Computer science—Mathematics. --- Annals --- Auxiliary sciences of history --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computer mathematics --- Electronic data processing --- Mathematics --- Chebyshev approximation. --- Gaussian quadrature formulas. --- Mathematicians.

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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area.   This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.   Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation   Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature   Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi.

Mathematical analysis. --- Numerical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Gautschi, Walter. --- Mathematicians -- Psychology. --- Mathematics. --- Computer science --- Approximation theory. --- Differential equations. --- History. --- Numerical Analysis. --- Mathematics of Computing. --- Approximations and Expansions. --- History of Mathematical Sciences. --- Ordinary Differential Equations. --- Computer science. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Informatics --- Computer science—Mathematics. --- Annals --- Auxiliary sciences of history --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computer mathematics --- Electronic data processing --- Mathematics --- Functions, Special. --- Interpolation. --- Mathematicians.