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Numerical solutions of algebraic equations --- Differential equations, Nonlinear --- Differential equations, Partial --- Iterative methods (Mathematics) --- Numerical solutions. --- 517 <061.3> --- 681.3*G15 --- Analysis--?<061.3> --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- Iterative methods (Mathematics). --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 517 <061.3> Analysis--?<061.3> --- Equations, Simultaneous --- Équations, Systèmes d' --- Équations, Systèmes d'. --- Analyse numérique. --- Numerical analysis --- Equations, Simultaneous. --- Analyse numérique --- Numerical analysis. --- Equations non lineaires --- Approximation des solutions

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Engineering --- Mathematics --- 681.3*G12 --- 681.3*G15 --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Data processing --- Computer. Automation

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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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Mathematical optimization --- Equations --- numerical solutions --- -Mathematical optimization --- 519.6 --- 681.3*G15 --- 681.3*G16 --- AA / International- internationaal --- 305.976 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algebra --- Mathematics --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Algoritmen. Optimisatie. --- Mathematical optimization. --- Basic Sciences. Statistics --- Numerical solutions. --- Probability Theory, Sampling Theory --- Probability Theory, Sampling Theory. --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Algoritmen. Optimisatie --- Graphic methods --- Equations - numerical solutions

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Differentiable dynamical systems. --- Nonlinear theories. --- Chaotic behavior in systems. --- 517.987 --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 681.3*G15 --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differentieerbare dynamicasystemen --- Systèmes dynamiques différentiables --- Chaotic behavior in systems --- Differentiable dynamical systems --- Nonlinear theories --- #KVIV:BB --- 681.3 *G18 --- 681.3*G17 --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Dynamics --- System theory --- Classical mechanics. Field theory --- Chaos --- Dynamique différentiable --- Théories non linéaires