Publication details
MATLAB Operators of Left/Right Division and Generalized Inverse
| Authors | |
|---|---|
| Year of publication | 1994 |
| Type | Article in Proceedings |
| Conference | Proceedings of the summer school MATLAB 93, Folia Fac. Sci. Nat. Univ. Masaryk. Brunensis, Mathematica 4 |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Least-squares solution of systems of linear equations; fast algorithm; generalized inverse; Moore-Penrose pseudoinverse |
| Description | For a non-square matrix $A$ the MATLAB operators of left ($\backslash$) or right (/) division yield a least-squares solution of matrix equations $AX=B$ or $XA=C$, respectively. The procedure for obtaining this solution is analyzed in detail and related to that obtained via the generalized inverse. The matrix $A^-=A\backslash I$, where $I$ is identity matrix, is shown to be a generalized 1-inverse (the first Moore-Penrose axiom $AA^-A=A$ holds) yielding with $A^-B$ the same least-squares solution as $A\backslash B$. A new effective algorithm based on that $A^-$ is developed for the computation of the Moore-Penrose pseudoinverse $A^+$ and listed as M-file 'rpinv' in appendix. The attached timing tests performed with large-scale matrices exhibit for 'rpinv' equal precision and times shorter by about 40% compared to MATLAB command 'pinv'. |
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