Chapter 9. Solution by Matrix Inversion

  1. J. Carlos Santamarina1 and
  2. Dante Fratta2

Published Online: 20 JUN 2006

DOI: 10.1002/0470021896.ch9

Discrete Signals and Inverse Problems: An Introduction for Engineers and Scientists

Discrete Signals and Inverse Problems: An Introduction for Engineers and Scientists

How to Cite

Santamarina, J. C. and Fratta, D. (2005) Solution by Matrix Inversion, in Discrete Signals and Inverse Problems: An Introduction for Engineers and Scientists, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/0470021896.ch9

Author Information

  1. 1

    Georgia Institute of Technology, USA

  2. 2

    University of Wisconsin-Madison, USA

Publication History

  1. Published Online: 20 JUN 2006
  2. Published Print: 1 JUL 2005

ISBN Information

Print ISBN: 9780470021873

Online ISBN: 9780470021897

SEARCH

Keywords:

  • matrix inversion solution;
  • inverse problem classification;
  • singular value decomposition (SVD);
  • least squares solution (LSS);
  • regularized least squares solution (RLSS);
  • nonnegative regularization coefficient;
  • nonlinearity;
  • inverse problem experimental design;
  • error propagation

Summary

This chapter contains sections titled:

  • Pseudoinverse

  • Classification of Inverse Problems

  • Least Squares Solution (LSS)

  • Regularized Least Squares Solution (RLSS)

  • Incorporating Additional Information

  • Solution Based on Singular Value Decomposition

  • Nonlinearity

  • Statistical Concepts – Error Propagation

  • Experimental Design for Inverse Problems

  • Methodology for the Solution of Inverse Problems

  • Summary

  • Further Reading

  • Solved Problems

  • Additional Problems