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We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
The problem of computing optimal orthogonal approximation to a given matrix has attracted growing interest in machine learning. Notable applications include the recent Muon optimizer or Riemannian optimization on the Stiefel manifold. Among…
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual…
The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Let $\phi$ be a psh function on a bounded pseudoconvex open set $\Omega \subset \C^n$, and let ${\cal I}(\phi)$ be the associated multiplier ideal sheaf. Motivated by resolution of singularities issues, we establish an effective version of…
We propose a new class of geometric invariants called jet vanishing orders, and use them to establish a new selection algorithm in the Kohn's construction of subelliptic multipliers for special domains in dimension $3$, inspired by the work…
In this paper new algorithm for calculating power indices is described. The complexity class of the problem is #P-complete and even calculating power index of the biggest player is NP-hard task. Constructed algorithm is a mix of ideas of…
Recently proposed implementations of quantum computer suffer from unavoidable interaction between quantum bits depending upon data being written in them. Novel procedure of avoiding multiqubit errors arising due to uncontrollable…
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. They can be considered as a generalization…
The team formation and routing problem is a challenging optimization problem with several real-world applications in fields such as airport, healthcare, and maintenance operations. To solve this problem, exact solution methods based on…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
To target challenges in differentiable optimization we analyze and propose strategies for derivatives of the Mat\'ern kernel with respect to the smoothness parameter. This problem is of high interest in Gaussian processes modelling due to…