On Frobenius normwise condition numbers for Moore-Penrose inverse and linear least-squares problems. (English) Zbl 1199.65128
Summary: Condition numbers play an important role in numerical analysis. Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using norms. In this paper, we give explicit, computable expressions depending on the data, for the normwise condition numbers for the computation of the Moore-Penrose inverse as well as for the solutions of linear least-squares problems with full-column rank.
MSC:
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
| 15A12 | Conditioning of matrices |
| 15A09 | Theory of matrix inversion and generalized inverses |
Software:
mctoolboxReferences:
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