Displaying similar documents to “Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix”

Best -term approximation in electronic structure calculations. II. Jastrow factors

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present a novel application of best -term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions ℱ ( 2 ) near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best -term approximation spaces A q α ( H 1 ) ,...

Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces

Nils Reich (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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For a class of anisotropic integrodifferential operators ℬ arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations ℬ on [0,1] with possibly large . Under certain conditions on ℬ , the scheme is of essentially optimal and dimension independent complexity 𝒪 ( | log |) without corrupting the convergence...

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

Unconditional biorthogonal wavelet bases in L p ( ℝ d )

Waldemar Pompe (2002)

Colloquium Mathematicae

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We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces L p ( ℝ d ) with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.

Adaptive convex optimization in Banach spaces: a multilevel approach

Claudio Canuto (2003)

Bollettino dell'Unione Matematica Italiana

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This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization...