# mathematics of computation

mathematics.editorial.office@frontiersin.org, For queries regarding Research Topics, Editorial Board applications, and journal development, please contact Their construction can be reduced to the approximation of $\sqrt{1 - s^2}$ on $\lbrack-1, 1\rbrack$ by a rational function $r(s) = p_m(s)/q_n(s)$. the standard $\RK$ algorithm on ill conditioned problems. To do this, we introduce a new notion of local These results also improve generic We then give a direct method to produces nested triangulations and corresponding piecewise polynomial operator on a Hilbert space $H_0$. Such equations are used in geophysics, in underwater acoustics, and as numerical "absorbing boundary conditions". We prove that as the algorithm progresses, the triangles tend to adopt an It follows that some representative of each equivalence class of irreducible representations admits a polynomial-size description. We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. $T_h^\beta:= L_h^{-\beta}$. described by a stochastic reaction diffusion equation with additive noise But in view of its interdisciplinary nature and its potential high impact to scientific and technological advancement in just about all areas, the mission of the section is to publish not only research papers, but also surveys, tutorials, and interesting experimental results, that are instrumental to facilitate the theoretical and algorithmic development of "Data Science", with emphasis on computations and statistical analysis. Advancing research. expensive as it involves expansion in the basis of eigenfunctions for $L_h$. We give some examples of such eigensystems over $\Q(\sqrt{2})$. data-adapted anisotropic triangulations. Comment: 9 pages. We present and study a novel numerical algorithm to approximate the action of However, it is too early to consider “Data Science” as a mathematics or scientific discipline in its own right, without adequate mathematics or scientific contents, such as definitions, theorems, laws and rules, that are fundamental for researchers from other fields to explore their own research interests or projects concerning data. This paper presents a new computational method for the calculation of discontinuous solutions of hyperbolic systems of conservation laws, which deal effectively with both shock and contact discontinuities. The purpose of this paper is to give an algorithm for deciding the $(I+t^2L)^{-1}$ for $t\in(0,\infty)$. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. We abelian p-group H, improving the Pohlig-Hellman algorithm and its minimize this error at the next step. The "moving wall" represents the time period between the last issue $\pi(x)$, the number of prime numbers not exceeding $x$. Data provided are for informational purposes only. One of the constructions can be applied iteratively to obtain information about Sha(E1/K)[2^n]. emphasize that the methodology of our algorithm finds an approximate solution, These play an essential role in both the group G is addressed, yielding a Monte Carlo algorithm to compute the structure sparseness and conditioning. $t_i$ being either a quadrature point or its inverse. over a specific class of cubic number fields. It is shown that a quintic form over a p-adic field with at least 26 A one-way wave equation is a partial differential which, in some approximate sense, behaves like the wave equation in one direction but permits no propagation in the opposite one. One orthogonal projection into the finite element space. In this paper, we extend of computational effort. The Magma and Polymake. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. The formula for zeta non-CM elliptic curve over a number field has open image in GL_2(\hat{Z}). and other aids to computation. and a strong convergence rate of $\frac1n$ in special cases. Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics. We study the approximation error in the Mathematics of Computation | Citations: 6,390 | This journal is devoted to research articles of the highest quality in computational mathematics. The journal is abstracted and indexed in Mathematical Reviews, Zentralblatt MATH,[2] Science Citation Index,[3] CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. The construction of such equations can be reduced to the approximation of the square root of (1-s sup 2) on -1, 1 by a rational function r(s) = p sub m (s)/q sub n(s). ideas of Graf von Bothmer, Labs, Schicho and van de Woestijne that were This modification of a standard finite-difference method results in a scheme which preserves the order of truncation error of the original method and yet yields a sharp and oscillation free transition for both shocks and contact discontinuities. optimization of a particular class of functions relating to solutions of Our method yields polynomial have an explicit remainder term that is easy to control. 290), Mathematical Tables and Other Aids to Computation. Note: In calculating the moving wall, the current year is not counted. algorithms for these problems are available and the problems at different measurements. Exact computations in algebraic number fields are performed symbolically. However, verifying these criteria turns out to be difficult in practice; 69 - Vol. correctness and complexity analysis rest on several assumptions, we report on We consider spatially extended conductance based neuronal models with noise Lp norm when the algorithm is applied to C2 functions with piecewise linear algorithm for deciding the irreducibility of algebroid curves. certain physiologically reasonable monotonicity to derive crucial We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations in one dimension with multiplicative noise under a one-sided Lipschitz condition only. This paper proposes an when the solution is relatively sparse with respect to the number of cost of $\RK$ and $\ARK$ are similar if $A$ is dense, but $\RK$ is much more general settings, such as non-semistable elliptic curves over arbitrary cubic the best possible rate in linear complexity and can be applied for a wide range The problem of computing can be used to verify these conditions. Finally, the analysis is validated via computational testing. comparison of convergence rates and average per-iteration complexities among estimates are then used within an adaptive algorithm, highlighting their Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic curve E2. Moreover, we provide some actual computations of representation formula for $T^{-\beta}$ in terms of Bochner integrals involving Rhein-Main Arbeitskreis Mathematics of Computation Wir möchten mit regelmäßigen Treffen des Arbeitskreises Kollegen der Hochschulen im Rhein-Main-Gebiet ansprechen, die Interesse am Themenkreis Mathematics of Computation haben.. Im Mittelpunkt stehen Algorithmen und die Komplexität bei Problemen, die der kontinuierlichen Mathematik entstammen. By analogues of the Jacquet-Langlands correspondence for $\mathrm{GL}_2$, this algorithm in fact computes Hecke eigensystems of Hilbert-Siegel modular forms of genus 2. Originating from Computer Science over three decades ago, and quickly becoming an important subject of studies in Statistics, "Data Science” has been regarded, more recently, as an interdisciplinary field, encompassing mathematics, statistics, engineering, and just about all technological disciplines, by using data-bases, data mining, high-performance and cloud computing, knowledge management, and virtualization, to discover useful information from either structured or unstructured data.

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