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 or...

In this paper we introduce the notion of orthogonally constant mapping in an isosceles orthogonal space and establish stability of orthogonally constant mappings. As an application, we discuss the orthogonal stability of the Pexiderized quadratic equation f(x + y) + g(x + y) = h(x) + k(y).

Abstract Understanding and considering refraction effects are important parts of the demanding task multimedia photogrammetry, especially with planar interfaces, so-called ”flat ports”. Yet, it remains challenging to determine reliable calibration results that both quickly acquired physically interpretable. In this contribution, a novel object-based optimization algorithm, relying on ray tracin...

For a ring R, denote by SpecΓ(κ,R) the κ-spectrum of the Γ-invariant of strongly uniform right R-modules. Recent realization techniques of Goodearl and Wehrung show that SpecΓ(א1 , R) is full for a suitable von Neumann regular algebra R, but the techniques do not extend to cardinals κ > א1. By a direct construction, we prove that for any field F and any regular uncountable cardinal κ there is a...

We consider C -compact orthogonally additive operators in vector lattices. After providing some examples of on a lattice with values Banach space we show that the set those is projection band Dedekind complete all regular operators. In second part article introduce new class lattices, called -complete, and any laterally-to-norm continuous operator from -complete to narrow, which generalizes res...

Convolutional approximate message-passing (CAMP) is an efficient algorithm to solve linear inverse problems. CAMP aims realize advantages of both (AMP) and orthogonal/vector AMP. uses the same low-complexity matched-filter as To asymptotic Gaussianity estimation errors for all right-orthogonally invariant matrices, guaranteed in AMP, Onsager correction AMP replaced with a convolution preceding ...

An orthogonal drawing of a plane graph G is a planar drawing of G, denoted by D(G), such that each vertex of G is drawn as a point on the plane, and each edge of G is drawn as a sequence of horizontal and vertical line segments with no crossings. An orthogonal polygon P is called orthogonally convex if the intersection of any horizontal or vertical line L and P is either a single line segment o...