Algorithm 686: FORTRAN subroutines for updating the QR decomposition
ACM Transactions on Mathematical Software (TOMS)
On recursive calculation of the generalized inverse of a matrix
ACM Transactions on Mathematical Software (TOMS)
Rounding error analysis of the classical Gram-Schmidt orthogonalization process
Numerische Mathematik
A swapping-based refinement of orthogonal matching pursuit strategies
Signal Processing - Sparse approximations in signal and image processing
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
The loss of orthogonality in the Gram-Schmidt orthogonalization process
Computers & Mathematics with Applications
On the Numerical Analysis of Oblique Projectors
SIAM Journal on Matrix Analysis and Applications
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A number of experiments are performed with the aim of enhancing a particular feature arising when biorthogonal sequences are used for the purpose of orthogonalization. It is shown that an orthogonalization process executed by biorthogonal sequences and followed by a re-orthogonalization step admits four numerically different realizations. The four possibilities are originated by the fact that, although an orthogonal projector is by definition a self-adjoint operator, due to numerical errors in finite precision arithmetic the biorthogonal representation does not fulfil such a property. In the experiments presented here one of the realizations is shown clearly numerically superior to the remaining three.