logo for matrixlab-examples.com
leftimage for matrixlab-examples.com

In-Place Matrix Inversion by Modified Gauss-Jordan Algorithm

D. DasGupta, M.Tech., M.ASCE, P.E., MCP

Former V.P.-Development, LEAP Software, Inc., Tampa, FL, USA
Former Principal Consultant, McDonnell Douglas Automation Co., St. Louis, MO, USA
Former Assistant Director, Central Water and Power Commission, New Delhi, India

REF: Applied Mathematics, 2013, 4, 1392-1396 http://dx.doi.org/10.4236/am.2013.410188 Published Online October 2013

     The classical Gauss-Jordan method for matrix inversion involves augmenting the matrix with a unit matrix and requires a workspace twice as large as the original matrix as well as computational operations to be performed on oth the original and the unit matrix. A modified version of the method for performing the inversion without explicitly generating the unit matrix by replicating its functionality within the original matrix space for more efficient utilization of computational resources is presented in this article.
     Although the algorithm described here picks the pivots solely from the diagonal which, therefore, may not contain a zero, it did not pose any problem for the author because he used it to invert structural stiffness matrices which met this requirement. Techniques such as row/column swapping to handle off-diagonal pivots are also applicable to this method but are beyond the scope of this article.

Keywords: Numerical Methods, Gauss-Jordan, Matrices, Inversion, In-Place, In-Core, Structural Analysis

Excerpt of the document:

Modified Gauss Jordan algorithm
classical matrix inversion 2
explanation of inversion 3
example of inversion

verification of inversion

in place, modified method for inversion

step 1 modified version
step 2
inversion complete after 3 iterations

 From 'Matrix Inversion' to home

 From 'Matrix Inversion' to Linear Algebra


footer for matlab page