Related papers: Approximation of integral operators using convolut…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…
We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical…
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…
Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…
We present techniques for speeding up the test-time evaluation of large convolutional networks, designed for object recognition tasks. These models deliver impressive accuracy but each image evaluation requires millions of floating point…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…