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 book 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.
Table of Contents
Foreword iPreface ii
Contributors iv
CHAPTERS
1 Exponential Data Fitting 01
Victor Pereyra and Godela Scherer
2 Computational Aspects of Exponential Data Fitting in Magnetic Resonance
Spectroscopy 27
Diana M. Sima, Jean-Baptiste Poullet and Sabine Van Huffel
3 Recovery of Relaxation Rates in MRI T2 - Weighted Brain Images
Via Exponential Fitting 52
Marco Paluszny, Marianela Lentini, Miguel Martin-Landrove, Wuilian Torres and
Rafael Martin
4 Exponential Time Series in Lattice Quantum Field Theory 71
Saul D. Cohen, Geroge T. Fleming and Huey-Wen Lin
5 Solving Separable Nonlinear Least Squares Problems with Multiple Datasets 94
Linda Kaufman
6 Sum-of-Exponentials Models for Time-Resolved Spectroscopy Data 110
Katharine M. Mullen and Ivo H. M. Van Stokkum
7 Two Exponential Models for Optically Stimulated Luminescence 128
Per Christian Hansen, Hans Bruun Nielsen, Christina Ankjaergaard and Mayank
Jain
8 Modelling Type Ia Supernova Light Curves 145
Bert W. Rust, Dianne P. O’Leary and Katharine M. Mullen
9 Accurate Calculations of the High-Frequency Impedance Matrix for VLSI
Interconnects and Inductors Above a Multi-Layer Substrate:
A VARPRO Success Story 165
Navin Srivastava, Robert Suaya, Victor Pereyra and Kaustav Banerjee
Index 193
