## Parameter Estimation and Inverse ProblemsParameter 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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Her zamanki yerlerde hiçbir eleştiri bulamadık.

### 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

algorithm applied approach approximate assume basis bound called Chapter columns compute condition consider continuous converge corresponding deconvolution defined Definition density derivative diagonal difference discrete discussed effect elements errors estimate Example Exercise expected value factorization Figure Fourier frequency function given gives important independent integral inverse problems inverse solution iterations least squares least squares problem least squares solution linear system mathematical maximum mean measurement method minimizing model parameters multiply noise nonlinear nonzero norm normally distributed Note observations obtain optimal orthogonal orthogonal matrix particular physical plot positive possible practice probability produce properties random variable referred regression require residual resolution resulting shown shows simple singular values solution solve standard deviation statistical Suppose symmetric matrix system of equations theorem Tikhonov regularization true model vector 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.