Proper nonnegative splittings over proper cones of rectangular matrices. (English) Zbl 1510.15002
The authors investigate the convergence of the iteration scheme associated to proper non-negative splittings and proper double non-negative splittings over proper cones. Comparison theorems for the spectral radii of matrices arising from proper non-negative splittings are deduced.
Furthermore, the authors apply their and previously known results to the regularized iterative method for ill-posed linear systems.
Reviewer: Julio Benítez Lopez (Valencia)
MSC:
| 15A06 | Linear equations (linear algebraic aspects) |
| 15A09 | Theory of matrix inversion and generalized inverses |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
Keywords:
rectangular matrix; proper cone; splitting; convergence; comparison theorem; Moore-Penrose inverseReferences:
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