Existence of best mean rational approximations

Existence of best simultaneous approximations in Lp(S, Σ, X)

Let (S,Σ , μ) be a complete positive σ -finite measure space and let X be a Banach space. We are concerned with the proximinality problem for the best simultaneous approximations to two functions in L p(S,Σ , X). Let Σ0 be a sub-σ -algebra of Σ and Y a nonempty locally weakly compact convex subset of X such that span Y and its dual have the Radon–Nikodym property. We prove that L p(S,Σ0, Y ) is...

The Existence of Rational Functions of Best Approximation*

Rational Approximations to Rational Models of Categorization

Can statistical machine learning theories and algorithms help explain human learning? Broadly speaking, machine learning studies the fundamental laws that govern all learning processes, including both artificial systems (e.g., computers) and natural systems (e.g., humans). It has long been understood that theories and algorithms from machine learning are relevant to understanding aspects of hum...

Rational Approximations to n

Using an IBM 1130 computer, we have generated the first 20,000 partial quotients in the ordinary continued-fraction representation of x.

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...