Related papers: A cache-friendly truncated FFT
This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor…
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\"o}nhage and Strassen designed an algorithm that improved the multiplication time for…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
This paper presents an architecture-friendly k-means clustering algorithm called SIVF for a large-scale and high-dimensional sparse data set. Algorithm efficiency on time is often measured by the number of costly operations such as…
We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance…
The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible)…
Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum field theories (QFTs). They have been used to solve…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$…
This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…
This study proposes the "adaptive flip graph algorithm", which combines adaptive searches with the flip graph algorithm for finding fast and efficient methods for matrix multiplication. The adaptive flip graph algorithm addresses the…
We develop a finite difference approximation of order $\alpha$ for the $\alpha$-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Gr\"unwald scheme. In particular,…
Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative…
We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…
This paper advances the computational efficiency of Deep Hedging frameworks through the novel integration of Kronecker-Factored Approximate Curvature (K-FAC) optimization. While recent literature has established Deep Hedging as a…
We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…