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We derive a Newton method for computing the best rank-(r1, r2, r3) approximation of a given J × K × L tensor A. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton’s method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds. We(More)
In this paper we present two algorithms for handwritten digit classification based on the higher order singular value decomposition (HOSVD). The first algorithm uses HOSVD for construction of the class models and achieves classification results with error rate lower than 6%. The second algorithm uses the HOSVD for tensor approximation simultaneously in two(More)
We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line(More)
Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) have attracted much attention and have been successfully applied to numerous data analysis problems where the components of the data are necessarily non-negative such as chemical concentrations in experimental results or pixels in digital images. Especially, Andersson and(More)
Ninety-seven patients were referred to the Toronto Hospital (Western Division) between January 1984 and January 1992 for selective angiographic embolization (108 embolizations, including repeat procedures) to control intractable or recurrent severe epistaxis. Eighty-one patients (comprising 94 embolizations) were referred on an emergent basis because of(More)
An orthogonal Procrustes problem on the Stiefel manifold is studied , where a matrix Q with orthonormal columns is to be found that minimizes kAQ ? Bk F for an l m matrix A and an l n matrix B with l m and m > n. Based on the normal and secular equations and the properties of the Stiefel manifold, necessary conditions for a global minimum, as well as(More)
We consider the problem of updating an invariant subspace of a Hermitian, large and struc-tured matrix when the matrix is modiied slightly. The problem can be formulated as that of computing stationary values of a certain function, with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann(More)
The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Eldén proposed an algorithm for this minimization problem based on a parametric programming reformulation involving the solution of a sequence of trust-region problems, and(More)