Related papers: Efficient Algorithms for Computing Rational First …
We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We give an approximate algorithm of computing holonomic systems of linear differential equations for definite integrals with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
Let $V$ be the set of real common solutions to $F = (f_1, \ldots, f_s)$ in $\mathbb{R}[x_1, \ldots, x_n]$ and $D$ be the maximum total degree of the $f_i$'s. We design an algorithm which on input $F$ computes the dimension of $V$. Letting…
We provide an algorithm which decides whether a polynomial foliation $\mathcal{F}^{\mathbb{C}^2}$ on the complex plane has a polynomial first integral of genus $g\neq 1$. Except in a specific case, an extension of the algorithm also decides…
First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high accuracy solutions, which creates a barrier to their use in…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible…
Solving the discrete logarithm problem in a finite prime field is an extremely important computing problem in modern cryptography. The hardness of solving the discrete logarithm problem in a finite prime field is the security foundation of…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…
The challenge of mapping indoor environments is addressed. Typical heuristic algorithms for solving the motion planning problem are frontier-based methods, that are especially effective when the environment is completely unknown. However,…