## Parameter Estimation and Inverse Problems, 1. ciltParameter 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 text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis. Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that contains Matlab code corresponding to all examples. * Designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background * Includes three appendices for review of linear algebra and crucial concepts in statistics * Battle-tested in courses at several universities *MATLAB exercises facilitate exploration of material |

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### İçindekiler

1 INTRODUCTION | 1 |

2 LINEAR REGRESSION | 15 |

3 DISCRETIZING CONTINUOUS INVERSE PROBLEMS | 41 |

4 RANK DEFICIENCY AND ILLCONDITIONING | 55 |

5 TIKHONOV REGULARIZATION | 89 |

6 ITERATIVE METHODS | 119 |

7 ADDITIONAL REGULARIZATION TECHNIQUES | 139 |

8 FOURIER TECHNIQUES | 153 |

11 BAYESIAN METHODS | 201 |

Appendix A REVIEW OF LINEAR ALGEBRA | 219 |

Appendix B REVIEW OF PROBABILITY AND STATISTICS | 251 |

Appendix C REVIEW OF VECTOR CALCULUS | 273 |

Appendix D GLOSSARY OF NOTATION | 281 |

283 | |

291 | |

International Geophysics Series | 297 |

### Diğer baskılar - Tümünü görüntüle

Parameter Estimation and Inverse Problems Richard C. Aster,Brian Borchers,Clifford H. Thurber Sınırlı önizleme - 2011 |

Parameter Estimation and Inverse Problems Richard C. Aster,Brian Borchers,Clifford H. Thurber Sınırlı önizleme - 2013 |

Parameter Estimation and Inverse Problems Richard C. Aster,Brian Borchers,Clifford H. Thurber Sınırlı önizleme - 2005 |

### Sık kullanılan terimler ve kelime öbekleri

approximate basis functions basis vectors Bayesian approach CGLS columns compute condition number confidence intervals consider converge convolution corresponding covariance matrix data points data set data vector diagonal discrete eigenvalues elements Example expected value Fourier transform frequency G matrix gradient ill-posed impulse response inverse problems inverse solution iterations L-curve Lagrange multiplier least squares problem least squares solution linear inverse problem linear regression linear system LM method mathematical model MATLAB maximum entropy regularization measurement errors minimizing minimum misfit model parameters mtrue Newton’s method noise nonlinear regression nonzero norm normal equations normally distributed null space obtain optimization problem orthogonal p-value parameter estimation posterior distribution prior distribution random variable ray path regularization parameter regularized solution residual seismic shown in Figure shows singular values solve spike model standard deviation statistical subspace system of equations theorem Tikhonov regularization tomography true model Volume zero

### Popüler pasajlar

Sayfa 288 - In G. Nolet, editor, Seismic Tomography with Applications in Global Seismology and Exploration Geophysics, chapter 3, pages 49-83.

Sayfa 288 - CF Van Loan. Generalizing the singular value decomposition. SIAM Journal on Numerical Analysis, 13:76-83, 1976.

Sayfa 288 - Leveque, J.-J., 1990. Simultaneous iterative reconstruction technique: physical interpretation based on the generalized least squares solution. J. Geophys. Res. 95, 12553-12559.