On the unconditional convergence of wavelet expansions for continuous functions

Fukuda, Naohiro; Kinoshita, Tamotu; Suzuki, Toshio

doi:10.1142/s0219691316500077

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2021

2023

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“…[5], [6], and [7]. Fukuda, Kinoshita, and Suzuki [8] have studied unconditional convergence of wavelet expansions. They have shown that uniformly convergent wavelet expansions even for continuous functions do not always converge unconditionally in L ∞ (R).…”

Section: Introductionmentioning

confidence: 99%

Electronic structure calculations with interpolating tensor product wavelet basis

Höynälänmaa¹,

Rantala²

2021

Preprint

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We introduce a basis set consisting of three-dimensional Deslauriers-Dubuc wavelets and numerically solve the Schrödinger equations of hydrogen atom, helium atom, hydrogen molecule ion, hydrogen molecule, and lithium hydride molecule with Hartree-Fock and DFT methods. We also compute the 2s and 2p excited states of hydrogen. The Coulomb singularity at the nucleus is handled by using a pseudopotential. Results are compared with those of CCCBDB and BigDFT. The eigenvalue problem is solved with Arnoldi and Lanczos methods, and the Poisson equation with GMRES and CGNR methods. The various matrix elements are computed using the biorthogonality relations of the interpolating wavelets.

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Section: Introductionmentioning

confidence: 99%