Preface; Symbols and Acronyms; 1. Setting the Stage. Problems With Ill-Conditioned Matrices; Ill-Posed and Inverse Problems; Prelude to Regularization; Four Test Problems; 2. Decompositions and Other Tools. The SVD and its Generalizations; Rank-Revealing Decompositions; Transformation to Standard Form; Computation of the SVE; 3. Methods for Rank-Deficient Problems. Numerical Rank; Truncated SVD and GSVD; Truncated Rank-Revealing Decompositions; Truncated Decompositions in Action; 4. Problems with Ill-Determined Rank. Characteristics of Discrete Ill-Posed Problems; Filter Factors; Working with Seminorms; The Resolution Matrix, Bias, and Variance; The Discrete Picard Condition; L-Curve Analysis; Random Test Matrices for Regularization Methods; The Analysis Tools in Action; 5. Direct Regularization Methods. Tikhonov Regularization; The Regularized General Gauss-Markov Linear Model; Truncated SVD and GSVD Again; Algorithms Based on Total Least Squares; Mollifier Methods; Other Direct Methods; Characterization of Regularization Methods; Direct Regularization Methods in Action; 6. Iterative Regularization Methods. Some Practicalities; Classical Stationary Iterative Methods; Regularizing CG Iterations; Convergence Properties of Regularizing CG Iterations; The LSQR Algorithm in Finite Precision; Hybrid Methods; Iterative Regularization Methods in Action; 7. Parameter-Choice Methods. Pragmatic Parameter Choice; The Discrepancy Principle; Methods Based on Error Estimation; Generalized Cross-Validation; The L-Curve Criterion; Parameter-Choice Methods in Action; Experimental Comparisons of the Methods; 8. Regularization Tools; Bibliography; Index.