Related papers: A Fast Algorithm for Computing the p-Curvature
Let $C$ be a genus $2$ curve with Jacobian isomorphic to the square of an elliptic curve with complex multiplication by a maximal order in an imaginary quadratic field of discriminant $-d<0$. We show that if the stable model of $C$ has bad…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
We state and analyze a generalization of the "truncation trick" suggested by Gourdon and Sebah to improve the performance of power series evaluation by binary splitting. It follows from our analysis that the values of D-finite functions…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
This paper introduces a novel class of fair and interpolatory curves called $p\kappa$-curves. These curves are comprised of smoothly stitched B\'ezier curve segments, where the curvature distribution of each segment is made to closely…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
In this article we give the details of an effective point counting algorithm for genus two curves over finite fields of characteristic three. The algorithm has an application in the context of curve based cryptography. One distinguished…
We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
We develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$, where $r$ is the…
Permutation tests are among the simplest and most widely used statistical tools. Their p-values can be computed by a straightforward sampling of permutations. However, this way of computing p-values is often so slow that it is replaced by…
Orthogonal systems in $\mathrm{L}_2(\mathbb{R})$, once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the differentiation…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$ where $r$ is the rank and $n$…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
We exhibit a condition-based analysis of the adaptive subdivision algorithm due to Plantinga and Vegter. The first complexity analysis of the PV Algorithm is due to Burr, Gao and Tsigaridas who proved a $O\big(2^{\tau d^{4}\log d}\big)$…