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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. Rankdeficient 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 illposed 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 rankdeficient and discrete illposed 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
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Modeles mathematiques.  Moindres carres  Statistik.  Methode der kleinsten Quadrate.  Mathematical models.  Least squares  Method of least squares  Squares, Least  Curve fitting  Geodesy  Mathematical statistics  Mathematics  Probabilities  Triangulation  Models, Mathematical  Simulation methods  Informatique.  Data processing.  Least squares.  Curve fitting.  Fitting, Curve  Numerical analysis  Smoothing (Numerical analysis)  Statistics  Graphic methods
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