Recently the L∞-norm optimization has been introduced to multi-view geometry to achieve global optimality. It is solved through solving a sequence of SOCP (second order cone programming) feasibility problem which needs sophisticated solvers and time consuming. This paper presents an efficient smooth approximation for L∞-norm optimization in multi-view geometry using log-sum-exp functions. We ha...

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that...

The operator of double differentiation, perturbed by the composition differentiation and a convolution one, on finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability recovering kernel from spectrum in weighted $L_2$-norm norm. For this purpose, we successively prove each step algorithm for solving inverse problem both norms. Besides justifying numerical co...

A Dirichlet boundary value problem for a linear parabolic differential equation is studied on a rectangular domain in the x− t plane. The coefficient of the second order space derivative is a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. It is proved that a numerical method, comprising a standard finite difference...

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure. A Banach space is said to have the fixed point property (FPP) if for every nonempty bounded closed convex C ⊂ X and every nonexpansive self-mapping T : C → C there is a fixed point of T in C. A Banach space is said to have the weak fixed point prope...

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those points x ∈ X such that A is not strongly regular at x. If E has no non-empty, perfect subsets then A is normal, and X is the character space of A. If X is ei...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...