Open AccessMixed and component wise condition numbers for weighted Moore-Penrose inverse and weighted least squares problems
Author(s) -
Li Zhao,
Jie Sun
Publication year - 2009
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil0901043z
Subject(s) - mathematics , condition number , inverse , moore–penrose pseudoinverse , rank (graph theory) , matrix (chemical analysis) , linear least squares , least squares function approximation , scaling , component (thermodynamics) , weighted geometric mean , norm (philosophy) , combinatorics , weighted arithmetic mean , statistics , linear model , eigenvalues and eigenvectors , geometry , physics , materials science , quantum mechanics , estimator , composite material , political science , law , thermodynamics
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. .