Martin Buhmann

most cited

ℓ^{1}

-summability and Fourier series of B-splines with respect to their knots

1 citations · 1 across the 3 of their papers we have counts for

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math.NA2024★ 2 cited

Compression using Quasi-Interpolation

Martin Buhmann, Feng Dai

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we…

math.NA2024

On Quasi-Interpolation and their associated shift-invariant space using a new class of generalized Thin Plate Splines and Inverse Multiquadrics

Mathis Ortmann, Martin Buhmann

A new generalization of shifted thin plate splines $φ (x) = (c^{2 d} + ∣∣ x ∣ ∣^{2 d}) lo g (c^{2 d} + ∣∣ x ∣ ∣^{2 d}), x \in R^{n}, d \in N, c > 0$ is presented to incr…

math.NA2023

High Accuracy Quasi-Interpolation using a new class of generalized Multiquadrics

Mathis Ortmann, Martin Buhmann

A new generalization of multiquadric functions $ϕ (x) = c^{2 d} + ∣∣ x ∣ ∣^{2 d}$ , where $x \in R^{n}$ , $c \in R$ , $d \in N$ , is presented to increase the accurac…

math.NA2023

New methods for quasi-interpolation approximations: resolution of odd-degree singularities

Martin Buhmann, Janin Jäger, Joaquín Jódar +1

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available…