The symmetric eigenvalue problem
The symmetric eigenvalue problem
Error Analysis of Direct Methods of Matrix Inversion
Journal of the ACM (JACM)
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy of Two Three-term and Three Two-term Recurrences for Krylov Space Solvers
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Rounding error analysis of the classical Gram-Schmidt orthogonalization process
Numerische Mathematik
Journal of Computational and Applied Mathematics
Block Gram-Schmidt Orthogonalization
SIAM Journal on Scientific Computing
Observations on oblique projectors and pseudoinverses
IEEE Transactions on Signal Processing
The application of an oblique-projected Landweber method to a model of supervised learning
Mathematical and Computer Modelling: An International Journal
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An oblique projector is an idempotent matrix whose null space is oblique to its range, in contrast to an orthogonal projector, whose null space is orthogonal to its range. Oblique projectors arise naturally in many applications and have a substantial literature. Missing from that literature, however, are systematic expositions of their numerical properties, including their perturbation theory, their various representations, their behavior in the presence of rounding error, the computation of complementary projections, and updating algorithms. This article is intended to make a start at filling this gap. The first part of the article is devoted to the first four of the above topics, with particular attention given to complementation. In the second part, stable algorithms are derived for updating an XQRY representation of projectors, which was introduced in the first part.