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  • 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'.
  • 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'. (en)
Title
  • MATLAB Operators of Left/Right Division and Generalized Inverse
  • MATLAB Operators of Left/Right Division and Generalized Inverse (en)
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  • MATLAB Operators of Left/Right Division and Generalized Inverse
  • MATLAB Operators of Left/Right Division and Generalized Inverse (en)
skos:notation
  • RIV/00216224:14310/94:00000309!RIV/2002/GA0/143102/N
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  • 25
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  • P(GA201/93/2408)
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  • Least-squares solution of systems of linear equations; fast algorithm; generalized inverse; Moore-Penrose pseudoinverse (en)
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  • [1E447B3FF9DF]
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  • Brno (Czech Rep.)
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  • Proceedings of the summer school MATLAB 93
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  • Veselý, Vítězslav
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  • Masarykova univerzita
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  • 80-210-1046-0
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  • 14310
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