Pseudo-inverse
by Bruno Luong
30 Sep 2009
(Updated 19 Oct 2009)
Factorize a matrix for pseudo-inverse calculation purpose
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| File Information |
| Description |
Factorize a matrix for pseudo-inverse to solve the normal equation:
A*x = 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-knot spline approximation
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| MATLAB release |
MATLAB 7.9 (2009b)
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| Other requirements |
Full object oriented supported Matlab version |
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| Comments and Ratings (1) |
| 28 Apr 2010 |
dm
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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 (?) |
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