Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) for high dimensional Markov decision processes (MDPs) arising in business applications. VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost, which can be used to assess the suboptimality of heuristic polici...

We prove the GSS conjecture of Garcia, Stillman and Sturmfels, which states that the ideal of the variety of secant lines to a Segre product of projective spaces is generated by 3 × 3 minors of flattenings. We also describe the decomposition of the coordinate ring of this variety as a sum of irreducible representations.

A generalization of the Seidel-Entringer-Arnold method for calculating the alternating permutation numbers (or secant-tangent numbers) leads to a new operation on sequences, the boustrophedon transform. This paper was published (in a somewhat different form) in J. Combinatorial Theory, Series A, 76 (1996), pp. 44–54. Present address: Mathematics Department, MIT, Cambridge, MA Present address: A...

In this paper we introduce a family of two-variable derivative polynomials for tangent and secant. Generating functions for the coefficients of this family of polynomials are studied. In particular, we establish a connection between these generating functions and Eulerian polynomials.

To Doron Zeilberger, with our warmest regards, on the occasion of his sixtieth birthday. Abstract. The secant and tangent numbers are given (t, q)-analogs with an explicit com-binatorial interpretation. This extends, both analytically and combinatorially, the classical evaluations of the Eulerian and Roselle polynomials at t = −1.

In this paper we give the full classification of irreducible projective threefolds whose k-secant variety has dimension smaller than the expected, for some k ≥ 2 (see theorem 0.1 below). As pointed out in the introduction, the case k = 1 was already known before.

In this paper we analyze the use of structured quasi-Newton formulae as preconditioners of iterative linear methods when the inexact-Newton approach is employed for solving nonlinear systems of equations. We prove that superlinear convergence and bounded work per iteration is obtained if the preconditioners satisfy a Dennis-Moré condition. We develop a theory of LeastChange Secant Update precon...