We study the approximation of a function class F in Lp by choosing first a basis B and then using n-term approximation with the elements of B. Into the competition for best bases we enter all greedy (i.e. democratic and unconditional [20]) bases for Lp. We show that if the function class F is well oriented with respect to a particular basis B then, in a certain sense, this basis is the best cho...

Theorems of the same type with greater constants on the right-hand side of (1.1) were proved by Hartman [3] and Koksma [6]. Recently, the author has shown [1] that the theorem of Uchiyama no longer holds if the constant s14 is replaced by any smaller number. Assuming weaker arithmetical restrictions in (1.2) on numerators and denominators of the approximants, the constant in (1.1) can be dimini...

We construct a new scheme of approximation of any multivalued algebraic function f(z) by a sequence {rn(z)}n∈N of rational functions. The latter sequence is generated by a recurrence relation which is completely determined by the algebraic equation satisfied by f(z). Compared to the usual Padé approximation our scheme has a number of advantages, such as simple computational procedures that allo...

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn R from scattered samples (xi; y = f(xi)) i=1....n, where first, w...

Long-term potentiation (LTP) and long-term depression (LTD) are persistent modifications of synaptic strength that have been implicated in learning, memory, and neuronal development. Despite their opposing effects, both forms of plasticity can be triggered by the activation of NMDA receptors. One mechanism proposed for this bidirectional response is that the specific patterns of afferent stimul...

Compressed Sensing decoding algorithms aim to reconstruct an unknown N dimensional vector x from m < N given measurements y = Φx, with an assumed sparsity constraint on x. All algorithms presently are iterative in nature, producing a sequence of approximations (s1, s2, ...) until a certain algorithm-specific stopping criterion is reached at iteration j∗, at which point the estimate x̂ = sj∗ is r...

The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrödinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrödinger equation can be reduced to the exactly solvable free-particle Schrödinger equation. The free-particle Sc...

We discuss best N-term approximation spaces for one-electron wavefunctions φi and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces Aq (H ) for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted q spa...

A self-consistent , non-perturbative scheme of approximation is proposed for arbitrary interacting quantum systems by generalization of the Hartree method.The scheme consists in approximating the original interaction term λHI by a suitable ’potential’ λV (φ) which satisfies the following two requirements: (i) the ’Hartree Hamiltonian’ Ho generated by V (φ) is exactly solvable i.e, the eigen sta...