International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 87392, 5 pages

A note on comprehensive backward biorthogonalization

David K. Ruch

Department of Mathematical and Computer Sciences, Metropolitan State College of Denver, University of Northern Colorado, Denver 80217-3362, CO, USA

Received 16 February 2006; Revised 21 July 2006; Accepted 25 July 2006

Copyright © 2006 David K. Ruch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a backward biorthogonalization technique for giving an orthogonal projection of a biorthogonal expansion onto a smaller subspace, reducing the dimension of the initial space by dropping d basis functions. We also determine which basis functions should be dropped to minimize the L2 distance between a given function and its projection. This generalizes some results in [3].