相关论文: A priori bounds for certified Krawczyk homotopy tr…

We introduce a new complexity measure of a path of (problems, solutions) pairs in terms of the length of the path in the condition metric which we define in the article. The measure gives an upper bound for the number of Newton steps…

This paper gives a priori estimates for the positve solutions of Kirchhoff type equation without variational structure.

The problem of composite hypothesis testing is considered in the context of Bayesian detection of weak target signals in cluttered backgrounds. (A specific example is the detection of sub-pixel targets in multispectral imagery.) In this…

Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we…

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach focuses on establishing a closed-loop…

The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither $H^2$-regularity nor $ L^{\infty} $-error estimation, but only $ H^1_0…

We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic incident wave. We introduce a potential for which the far field…

In this paper we prove a priori and a posteriori error estimates for a multiscale numerical method for computing equilibria of multilattices under an external force. The error estimates are derived in a $W^{1,\infty}$ norm in one space…

We study the problem of coordinating multiple robots along fixed geometric paths. Our contribution is threefold. First we formalize the intuitive concept of priorities as a binary relation induced by a feasible coordination solution,…

We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…

We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…

Direct collocation for Bolza optimal control yields discrete Karush-Kuhn-Tucker (KKT) points, while practical solvers expose only discrete quantities such as primal-dual iterates, reduced Hessians, and Jacobians. This creates a gap between…

Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as…

In this paper we proposed the homotopy approach for solving the nonlinear Balitsky-Kovchegov (BK) evolution equation with running QCD coupling. The approach consists of two steps. First, is the analytic solution to the nonlinear evolution…

A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…

In this note an improvement of the Katz's bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem to estimating the number of rational points on certain toric…

The complex software systems developed nowadays require assessing their quality and proneness to errors. Reducing code complexity is a never-ending problem, especially in today's fast pace of software systems development. Therefore, the…

We propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by…

Graded path modalities count the number of paths satisfying a property, and generalize the existential (E) and universal (A) path modalities of CTL*. The resulting logic is called GCTL*. We settle the complexity of satisfiability of GCTL*,…

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds…