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Numerical analysis --- Mathematical statistics --- Equations, Simultaneous --- Least squares --- Moindres carrés --- Numerical solutions --- Least squares. --- Numerical solutions. --- 519.65 --- -Least squares --- #TELE:SISTA --- Method of least squares --- Squares, Least --- Curve fitting --- Geodesy --- Mathematics --- Probabilities --- Triangulation --- Simultaneous equations --- Approximation. Interpolation --- 519.65 Approximation. Interpolation --- Moindres carrés --- Numerical calculations --- Calculs numériques --- Moindres carrés. --- Calculs numériques. --- Analyse numérique. --- Algèbre linéaire. --- Algebras, Linear --- Equations, Simultaneous - Numerical solutions. --- Acqui 2006 --- Equations, Simultaneous. Numerical solutions
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Iterative methods (Mathematics) --- Equations, Simultaneous --- Numerical solutions --- Simultaneous equations --- 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 --- 681.3*G13 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Iteration (Mathematics) --- Numerical analysis --- Iterative methods (Mathematics). --- Numerical solutions. --- Itération (Mathématiques) --- Equations, Simultaneous - Numerical solutions
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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
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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Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and the efficiency and reliability of the computations.
Equations, Simultaneous --- Iterative methods (Mathematics) --- Sparse matrices. --- Itération (Mathématiques) --- Matrices éparses --- Numerical solutions. --- 519.6 --- 681.3*G13 --- 517.95 --- #TELE:SISTA --- 681.3*G15 --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Partial differential equations --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 517.95 Partial differential equations --- 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 --- Iterative methods (Mathematics). --- Itération (Mathématiques) --- Matrices éparses --- Sparse matrices --- Spare matrix techniques --- Matrices --- Iteration (Mathematics) --- Numerical analysis --- Numerical solutions --- Equations, Simultaneous - Numerical solutions.
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