The Orthogonally Constrained Regression Revisited
نویسندگان
چکیده
Two data analysis problems the orthonormal Procrustes problem and the Penrose regression problem are reconsidered in this paper These problems are known in the literature for their importance as well as di culty This work presents a way to calculate the projected gradient and the projected Hessian explicitly One immediate result of this calculation is the complete characterization of the rst order and the second order optimality conditions for both problems Another application is the natural formulation of a continuous steepest descent ow that can serve as a globally convergent numerical method Applications are demonstrated by numerical examples
منابع مشابه
Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras
In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.
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