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Pseudo-inverse

30 Sep 2009 (Updated 19 Oct 2009)

Factorize a matrix for pseudo-inverse calculation purpose

File Information
Description	Factorize a matrix for pseudo-inverse to solve the normal equation: Ax = b There are two advantages of pseudo-inverse compared to MATLAB pinv: - PINV requires costly SVD - PINV does not operated with sparse matrix. The solution x minimize the 2-norm of the residual \|Ax - b\|. In case of underdetermined system, i.e., rank(A) < length(x), the solution returned by pseudoinverse(A)b is the least 2-norm among all solutions. Note that this property does not meet if backslash operator is used: x = A\b. Method: Use QR factorization on both source and destination space. The factorized result is stored in object that can be used later to multiply with any target space vectors (RHS). Inspired from FACTORIZE http://www.mathworks.com/matlabcentral/fileexchange/24119
Acknowledgements	This submission has inspired the following: Free-knots spline approximation
MATLAB release	MATLAB 7.9 (2009b)
Other requirements	Full object oriented supported Matlab version
Zip File Content
Other Files	license.txt, PseudoInverseFolder/@pseudoinverse/private/getoption.m, PseudoInverseFolder/@pseudoinverse/private/lowercase.m, PseudoInverseFolder/@pseudoinverse/pseudoinverse.m

Tags for This File
Everyone's Tags	leastsquares, minimum norm, moorepenrose, pseudoinverse, qr, regularization, tikhonov
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Updates
05 Oct 2009	New description + Iterative method with Tkhonov regularization
09 Oct 2009	Change the code structure (private function instead of static methods) for better compatible with older Matlab versions
18 Oct 2009	New methods supported: left/right multiplication, conjugate, transpose, and complex-transpose
19 Oct 2009	Detect SuiteSparseQR package to carry out QR factorization on sparse matrix, not available for Matlab prior 2009B (?)

Tag Activity for this File
Tag	Applied By	Date/Time
moorepenrose	Bruno Luong	30 Sep 2009 10:23:57
pseudoinverse	Bruno Luong	30 Sep 2009 10:23:57
qr	Bruno Luong	30 Sep 2009 10:23:57
minimum norm	Bruno Luong	30 Sep 2009 10:23:57
regularization	Bruno Luong	17 Oct 2009 02:47:12
leastsquares	Bruno Luong	19 Oct 2009 09:32:02
tikhonov	Bruno Luong	19 Oct 2009 17:23:13

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