UID:
almahu_9948026795102882
Format:
1 online resource (315 p.)
ISBN:
1-280-96117-1
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9786610961177
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0-08-047055-6
Series Statement:
International geophysics series ; ; v. 90
Content:
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The t
Note:
Description based upon print version of record.
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Cover; Contents; Preface; 1 INTRODUCTION; 1.1 CLASSIFICATION OF INVERSE PROBLEMS; 1.2 EXAMPLES OF PARAMETER ESTIMATION PROBLEMS; 1.3 EXAMPLES OF INVERSE PROBLEMS; 1.4 WHY INVERSE PROBLEMS ARE HARD; 1.5 EXERCISES; 1.6 NOTES AND FURTHER READING; 2 LINEAR REGRESSION; 2.1 INTRODUCTION TO LINEAR REGRESSION; 2.2 STATISTICAL ASPECTS OF LEAST SQUARES; 2.3 UNKNOWN MEASUREMENT STANDARD DEVIATIONS; 2.4 L1 REGRESSION; 2.5 MONTE CARLO ERROR PROPAGATION; 2.6 EXERCISES; 2.7 NOTES AND FURTHER READING; 3 DISCRETIZING CONTINUOUS INVERSE PROBLEMS; 3.1 INTEGRAL EQUATIONS; 3.2 QUADRATURE METHODS
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3.3 EXPANSION IN TERMS OF REPRESENTERS3.4 EXPANSION IN TERMS OF ORTHONORMAL BASIS FUNCTIONS; 3.5 THE METHOD OF BACKUS AND GILBERT; 3.6 EXERCISES; 3.7 NOTES AND FURTHER READING; 4 RANK DEFICIENCY AND ILL-CONDITIONING; 4.1 THE SVD AND THE GENERALIZED INVERSE; 4.2 COVARIANCE AND RESOLUTION OF THE GENERALIZED INVERSE SOLUTION; 4.3 INSTABILITY OF THE GENERALIZED INVERSE SOLUTION; 4.4 AN EXAMPLE OF A RANK-DEFICIENT PROBLEM; 4.5 DISCRETE ILL-POSED PROBLEMS; 4.6 EXERCISES; 4.7 NOTES AND FURTHER READING; 5 TIKHONOV REGULARIZATION; 5.1 SELECTING A GOOD SOLUTION
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5.2 SVD IMPLEMENTATION OF TIKHONOV REGULARIZATION5.3 RESOLUTION, BIAS, AND UNCERTAINTY IN THE TIKHONOV SOLUTION; 5.4 HIGHER-ORDER TIKHONOV REGULARIZATION; 5.5 RESOLUTION IN HIGHER-ORDER TIKHONOV REGULARIZATION; 5.6 THE TGSVD METHOD; 5.7 GENERALIZED CROSS VALIDATION; 5.8 ERROR BOUNDS; 5.9 EXERCISES; 5.10 NOTES AND FURTHER READING; 6 ITERATIVE METHODS; 6.1 INTRODUCTION; 6.2 ITERATIVE METHODS FOR TOMOGRAPHY PROBLEMS; 6.3 THE CONJUGATE GRADIENT METHOD; 6.4 THE CGLS METHOD; 6.5 EXERCISES; 6.6 NOTES AND FURTHER READING; 7 ADDITIONAL REGULARIZATION TECHNIQUES; 7.1 USING BOUNDS AS CONSTRAINTS
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7.2 MAXIMUM ENTROPY REGULARIZATION7.3 TOTAL VARIATION; 7.4 EXERCISES; 7.5 NOTES AND FURTHER READING; 8 FOURIER TECHNIQUES; 8.1 LINEAR SYSTEMS IN THE TIME AND FREQUENCY DOMAINS; 8.2 DECONVOLUTION FROMA FOURIER PERSPECTIVE; 8.3 LINEAR SYSTEMS IN DISCRETE TIME; 8.4 WATER LEVEL REGULARIZATION; 8.5 EXERCISES; 8.6 NOTES AND FURTHER READING; 9 NONLINEAR REGRESSION; 9.1 NEWTON'S METHOD; 9.2 THE GAUSS-NEWTON AND LEVENBERG-MARQUARDT METHODS; 9.3 STATISTICAL ASPECTS; 9.4 IMPLEMENTATION ISSUES; 9.5 EXERCISES; 9.6 NOTES AND FURTHER READING; 10 NONLINEAR INVERSE PROBLEMS
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10.1 REGULARIZING NONLINEAR LEAST SQUARES PROBLEMS10.2 OCCAM'S INVERSION; 10.3 EXERCISES; 10.4 NOTES AND FURTHER READING; 11 BAYESIAN METHODS; 11.1 REVIEW OF THE CLASSICAL APPROACH; 11.2 THE BAYESIAN APPROACH; 11.3 THE MULTIVARIATE NORMAL CASE; 11.4 MAXIMUM ENTROPY METHODS; 11.5 EPILOGUE; 11.6 EXERCISES; 11.7 NOTES AND FURTHER READING; Appendix A REVIEW OF LINEAR ALGEBRA; A.1 SYSTEMS OF LINEAR EQUATIONS; A.2 MATRIX AND VECTOR ALGEBRA; A.3 LINEAR INDEPENDENCE; A.4 SUBSPACES OF Rn; A.5 ORTHOGONALITY AND THE DOT PRODUCT; A.6 EIGENVALUES AND EIGENVECTORS; A.7 VECTOR AND MATRIX NORMS
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A.8 THE CONDITION NUMBER OF A LINEAR SYSTEM
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English
Additional Edition:
ISBN 0-12-065604-3
Language:
English
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