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Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates…
There is an increasing need for algorithms that can accurately detect changepoints in long time-series, or equivalent, data. Many common approaches to detecting changepoints, for example based on penalised likelihood or minimum description…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
This extended abstract gives a construction for lifting a Gr\"obner basis algorithm for an ideal in a polynomial ring over a commutative ring R under the condition that R also admits a Gr\"obner basis for every ideal in R.
A Grobner basis-based algorithm for solving the Frobenius Instance Problem is presented, and this leads to an algorithm for solving the Frobenius Problem that can handle numbers with thousands of digits. Connections to irreducible…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We construct neural network regression models to predict key metrics of complexity for Gr\"obner bases of binomial ideals. This work illustrates why predictions with neural networks from Gr\"obner computations are not a straightforward…
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…
Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been…
In this paper, we make a contribution to the computation of Gr\"obner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…
In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Over the last decade, implementations of several desingularization algorithms have appeared in various contexts. These differ as widely in their methods and in their practical efficiency as they differ in the situations in which they may be…