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A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher…
The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outputs and observations. The gradients required by the numerical…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether $\alpha,\beta$ or $\alpha\pm\beta$ assume integer values. Exceptional Jacobi…
Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…
A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them…
We show how all the quantal systems related to the exceptional Laguerre and Jacobi polynomials can be constructed in a direct and systematic way, without the need of shape invariance and Darboux-Crum transformation. Furthermore, the…
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…
In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit…
We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amounting to two matrix-matrix multiplications) and solves the…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the…
We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseur, M. Webb and Z. Zhou, SIAM J. Matrix Anal. Appl. 46…
In this paper we study various difference equations related to Jacobi-type pencils. By a Jacobi-type pencil one means the following pencil: $J_5 - \lambda J_3$, where $J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…