Inverse and ill-posed problems

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Front Cover; Inverse and Ill-Posed Problems; Copyright Page; Table of Contents; Contributors; Preface; CHAPTER 1. A FEW GEOMETRICAL FEATURES OF INVERSE AND ILL-POSED PROBLEMS; I. INTRODUCTION; II. WELL-POSED QUESTIONS FOR (STRONGLY) ILL-POSED PROBLEMS; III. JOINT GENERALIZED COORDINATES; IV. JOINT TRAJECTORIES; REFERENCES; CHAPTER 2. THE INVERSE PROBLEM OF AQUIFER TRANSMISSIVITY IDENTIFICATION; ABSTRACT; 1. INTRODUCTION; 2. COMPUTATIONAL METHODS FOR TRANSMISSIVITY IDENTIFICATION; 3. THE LINEAR FUNCTIONAL STRATEGY; ACKNOWLEDGEMENT; REFERENCES CHAPTER 3. RELIABILITY OF INFORMATION OBTAINED FROM APPROXIMATELY-SOLVED PROBLEMSI. ANALYSIS OF APPROXIMATE SOLUTIONS; II. APPROXIMATE SOLUTION SETS; III. PRACTICAL IMPLICATIONS; REFERENCES; CHAPTER 4. THREE TOPICS IN ILL-POSED PROBLEMS; I. INTRODUCTION; II. PARTIAL SPLINE METHODS FOR INCLUDING DISCONTINUITIES IN OTHERWISE SMOOTH REGULARIZED SOLUTIONS OF ILL POSED PROBLEMS WITH NOISY DATA; III. COMPUTATIONAL PROBLEMS COMMON TO PARTIAL SPLINE MODELS; IV. THE USE OF GCV AS A STOPPING RULE IN THE ITERATIVE SOLUTION OF LARGE LINEAR SYSTEMS. v. GCV AND CONSTRAINED REGULARIZATION FOR THE PARAMETER ESTIMATION PROBLEMREFERENCES; CHAPTER 5. A NEW APPROACH TO CLASSIFICATION AND REGULARIZATION OF ILL-POSED OPERATOR EQUATIONS; 1. INTRODUCTION; 2. ON THE ROLE OF OUTER INVERSES IN ""SOLVABILITY"" AND ""REGULAJRIZATION"" OF ILL-POSED PROBLEMS; 3. REGULARIZERS OF TYPES I AND II. APPROXIMATE OUTER AND APPROXIMATE RIGHT INVERSES; 4. CHARACTERIZATIONS OF ILL-POSED PROBLEMS OF TYPE I OR II; 5. REMARKS; REFERENCES; CHAPTER 6. ON THE OPTIMALITY OF REGULARIZATION METHODS; I. INTRODUCTION; II . OPTIMALITY DEFINITIONS: POLLUTED RIGHT-HAND TERM III. OPTIMALITY DEFINITIONS: OPERATOR POLLUTED ALSOIV. CONSTRUCTION OP OL-OPTIMAL METHODS; V. QUASIOPTIMALITY CONDITIONS; VI. OPTIMALITY OP TIKHONOV METHOD; VII. QUASIOPTIMAL CHOICES OF PARAMETER IN TIKHONOV METHOD; VIII. OPTIMALITY ON THE SOURCE SETS; IX. OPTIMALITY OP LAVRENTIEV, TIKHONOV AND ITERATION METHODS ON SOURCE SETS; X. DISCREPANCY PRINCIPLE AND QUASIOPTIMALITY ON SOURCE SETS; REFERENCES; CHAPTER 7. OPTIMAL PARAMETER CHOICE FOR ORDINARY AND ITERATED TIKHONOV REGULAR!ZATION; ABSTRACT; I. INTRODUCTION; II. PARAMETER CHOICE FOR ITERATED TIKHONOV REGULARIZATION III. A VARIANT OF MARTI'S METHODREFERENCES; CHAPTER 8. PARAMETER CHOICE FOR TIKHONOV REGULARIZATION OF ILL-POSED PROBLEMS; ABSTRACT; 1. INTRODUCTION; 2. OPTIMAL CHOICE OF THE REGULARIZATION PARAMETER FOR ITERATED TIKHONOV REGULARIZATION; 3. FINITE DIMENSIONAL APPROXIMATIONS; REFERENCES; CHAPTER 9. FREDHOLM INTEGRAL EQUATIONS OF FIRST KIND AND THE METHOD OF CORRELOGRAM; 0. INTRODUCTION; I. ASYMPTOTIC CONVERGENCE OF EIGENFUNCTION EXPANSIONS; II. PROBABILISTIC METHODS; III. THE METHOD OF CORRELOGRAM; REFERENCES; CHAPTER 10. ON ILL-POSED PROBLEMS AND THE METHOD OF CONJUGATE GRADIENTS