MultiPrecisionArrays. jl is a Julia package.

Numerical Analysis Numerical Analysis 65F05, 65F10, 45B05, 45G10

For the case with quadratic generation cost our algorithm is significantly faster than solving the problem by a state-of-the-art MIL(Q)P formulation.

Optimization and Control

Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials.

Numerical Analysis Numerical Analysis

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations.

Numerical Analysis Numerical Analysis

We prove that, up to isomorphism, there are exactly 75 traingulations of $\mathbb{HP}^2$ with 15 vertices and symmetry group of order at least 4: the three Brehm-K\"uhnel triangulations and the 72 new triangulations listed above.

Combinatorics Computational Geometry Geometric Topology 57Q15, 57Q70, 05E45, 55M35

We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L^2.

Numerical Analysis Numerical Analysis

We prove and collect numerous explicit and computable results for the fractional Laplacian $(-\Delta)^s f(x)$ with $s>0$ as well as its whole space inverse, the Riesz potential, $(-\Delta)^{-s}f(x)$ with $s\in\left(0,\frac{1}{2}\right)$.

Numerical Analysis Numerical Analysis

Inspired by the Continuous Basis Pursuit (C-BP) method, our approach introduces an extra parameter to account for the shift of the sources between grid locations.

Optimization and Control

After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties.

Algebraic Geometry

Numerical methods for computing the solutions of Markov backward stochastic differential equations (BSDEs) driven by continuous-time Markov chains (CTMCs) are explored.

Probability Numerical Analysis Numerical Analysis Mathematical Finance