scholarly journals Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems

1992 ◽  
Vol 161 ◽  
pp. 27-43 ◽  
Author(s):  
Musheng Wei
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Problems ◽  
Algebraic Properties

scholarly journals Mixed and component wise condition numbers for weighted Moore-Penrose inverse and weighted least squares problems

Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Li Zhao ◽  
Jie Sun
Keyword(s):  
Numerical Analysis ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Full Column Rank ◽  
Condition Numbers ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Linear Least Squares Problem ◽  
Classical Condition ◽  
The Matrix

Condition numbers play an important role in numerical analysis. Classical condition numbers are norm-wise: they measure both input perturbations and output errors with norms. To take into account the relative scaling of data components or a possible sparseness, component-wise condition numbers have been increasingly considered. In this paper, we give explicit expressions for the mixed and component-wise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem ||W 1 2 (Ax-b) ||2 = minv2Rn ||W 1 2 (Av-b) ||2, where the matrix A with full column rank. .

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