Parameter Estimation and Inverse Problems

Ön Kapak
Elsevier, 25 Oca 2005 - 320 sayfa

Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology.

It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems, with particular attention to computational, mathematical, and statistical issues related to their application to geophysical problems. Four appendices review foundational concepts in linear algebra, statistics, vector calculus, and notation. Pedagogy includes hundreds of highlighted equations, examples, and definitions; introductory chapter synopses; end-of-chapter exercises, both programming and theoretical; and suggestions for further reading.

The text is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background.

  • 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
 

Seçilmiş sayfalar

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
BIBLIOGRAPHY
283
INDEX
291
International Geophysics Series
297

9 NONLINEAR REGRESSION
171
10 NONLINEAR INVERSE PROBLEMS
191
About the CDROM
303
Telif Hakkı

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, 1. cilt
Richard C. Aster,Clifford H. Thurber,Brian Borchers
Sınırlı önizleme - 2005
Tümünü görüntüle »

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 solve standard deviation statistical Suppose symmetric matrix system of equations theorem Tikhonov regularization transform true model vector Volume written zero

Yazar hakkında (2005)

Professor Aster is an Earth scientist with broad interests in geophysics, seismological imaging and source studies, and Earth processes. His work has included significant field research in western North America, Italy, and Antarctica. Professor Aster also has strong teaching and research interests in geophysical inverse and signal processing methods and is the lead author on the previous two editions. Aster was on the Seismological Society of America Board of Directors, 2008-2014 and won the IRIS Leadership Award, 2014.

Dr. Borchers’ primary research and teaching interests are in optimization and inverse problems. He teaches a number of undergraduate and graduate courses at NMT in linear programming, nonlinear programming, time series analysis, and geophysical inverse problems. Dr. Borchers’ research has focused on interior point methods for linear and semidefinite programming and applications of these techniques to combinatorial optimization problems. He has also done work on inverse problems in geophysics and hydrology using linear and nonlinear least squares and Tikhonov regularization.

Professor Thurber is an international leader in research on three-dimensional seismic imaging ("seismic tomography") using earthquakes. His primary research interests are in the application of seismic tomography to fault zones, volcanoes, and subduction zones, with a long-term focus on the San Andreas fault in central California and volcanoes in Hawaii and Alaska. Other areas of expertise include earthquake location (the topic of a book he edited) and geophysical inverse theory.

Kaynakça bilgileri

BaşlıkParameter Estimation and Inverse Problems
90. cilt/International Geophysics
YazarlarRichard C. Aster, Brian Borchers, Clifford H. Thurber
YayıncıElsevier, 2005
ISBN0080470556, 9780080470559
Uzunluk320 sayfa
  
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