Characterization for best nonlinear approximations: A geometrical interpretation

New Characterization for Nonlinear Weighted Best Simultaneous Approximation

The problem of best simultaneous approximation has a long history and continues to generate much interest. The problem of approximating simultaneously two continuous functions on a finite closed interval was first studied by Dunham 1 . Since then, such problems have been extended extensively, see, for example, 1–7 and references therein. In particular, characterization and uniqueness results we...

Best subspace tensor approximations

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained via the singular value decomposition which allows to compute the best rank k approximations. For t-tensors with t > 2 many generalizations of the singular val...

A geometrical interpretation of the inverse matrix

A New Geometrical Interpretation of Trilinear Constraints

We give a new geometrical interpretation of the well-known algebraic trilinear constraints used in motion analysis from three views observation. We show that those algebraic equations correspond to depth errors appropriately weighted by a function of the relative reliability of the corresponding measurements. Therefore directly minimizing the algebraic trilinear equations, in the least squares ...

Geometrical Interpretation of Constrained Systems

The standard approach to classical dynamics is to form a Lagrangian which is a function of n generalized coordinates qi, n generalized velocities q̇i and parameter τ . The 2n variables qi, q̇i form the tangent bundle TQ. The passage from TQ to the cotangent bundle T ∗Q is achieved by introducing generalized momenta and a Hamiltonian. However, this procedure requires that the rank of Hessian matrix