Editors: Victor Pereyra, Godela Scherer

Exponential Data Fitting and its Applications

eBook: US $59 Special Offer (PDF + Printed Copy): US $148
Printed Copy: US $119
Library License: US $236
ISBN: 978-1-60805-345-2 (Print)
ISBN: 978-1-60805-048-2 (Online)
Year of Publication: 2010
DOI: 10.2174/97816080504821100101


Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. The most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. A number of different methods have been proposed through the years to solve these types of problems and new applications appear daily. Necessary guidance is provided so that care should be taken when applying standard or simplified methods to it. The described methods take into account the separability between the linear and nonlinear parameters, which have been quite successful. The accessibility of good, publicly available software that has been very beneficial in many different fields is also considered. This Ebook covers the main solution methods (Variable Projections, Modified Prony) and also emphasizes the applications to different fields. It is considered essential reading for researchers and students in this field.


- Pp. i
Michael Saunders
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- Pp. ii-iii (2)
Victor Pereyra, Mountain View, Godela Scherer
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- Pp. iv-vi (3)
V. Pereyra, G. Scherer
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Exponential data fitting

- Pp. 1-26 (26)
Victor Pereyra, Godela Scherer
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Computational aspects of exponential data fitting in Magnetic Resonance Spectroscopy

- Pp. 27-51 (25)
Diana M. Sima, Jean-Baptiste Poullet, Sabine Van Huffel
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Recovery of relaxation rates in MRI T2-weighted brain images via exponential fitting

- Pp. 52-70 (19)
Marco Paluszny, Marianela Lentini, Miguel Martin-Landrove, Wuilian Torres, Rafael Martin
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Exponential time series in lattice quantum field theory

- Pp. 71-93 (23)
Saul D. Cohen, George T. Fleming, Huey-Wen Lin
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Solving separable nonlinear least squares problems with multiple datasets

- Pp. 94-109 (16)
Linda Kaufman
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Sum-of-exponentials models for time-resolved spectroscopy data

- Pp. 110-127 (18)
Katharine M. Mullen, Ivo H. M. van Stokkum
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Two exponential models for optically stimulated luminescence

- Pp. 128-144 (17)
Per Christian Hansen, Hans Bruun Nielsen, Christina Ankjærgaard, Mayank Jain
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Modelling type Ia supernova light curves

- Pp. 145-164 (20)
Bert W. Rust, Dianne P. O’Leary, Katharine M. Mullen
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Accurate calculations of the high-frequency impedance matrix for VLSI interconnects and inductors above a multi-layer substrate:

- Pp. 165-192 (28)
Navin Srivastava, Roberto Suaya, Victor Pereyra
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- Pp. 193-195 (3)
V. Pereyra, G. Scherer
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.An Introduction to Sobolev Spaces.
.Exterior Calculus: Theory and Cases.
.Trefftz and Fundamental Solution-Based Finite Element Methods.
.The Generalized Relative Gol’dberg Order and Type: Some Remarks on Functions of Complex Variables.