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Numerical solutions of algebraic equations --- Sparse matrices --- FORTRAN (Computer program language) --- Matrices éparses --- FORTRAN (Langage de programmation) --- Data processing. --- Informatique --- data processing --- #TCPW N2.0 --- 519.6 --- 681.3*G --- 681.3*G13 --- Computational mathematics. Numerical analysis. Computer programming --- Mathematics of computing --- 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 --- 681.3*G Mathematics of computing --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Matrices éparses --- Spare matrix techniques --- Matrices --- Formula Translation (Computer program language) --- Programming languages (Electronic computers) --- Data processing --- Sparse matrices - data processing

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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.