Given a matrix $A \in \mathbb{R}^{n\times n}$, we consider the problem of maximizing $x^TAx$ subject to constraint $x \{-1,1\}^n$. This problem, called MaxQP by Charikar and Wirth [FOCS'04], generalizes MaxCut has natural applications in data clustering study disordered magnetic phases matter. showed that admits an $\Omega(1/\lg n)$ approximation via semidefinite programming, Alon, Makarychev, ...

The approximating sequence Riccati equation method is an efficient approach for solving the nonlinear optimal control problems, but its neglect of dynamics and necessary optimality condition makes law difficult to satisfy optimality. In this paper, pseudospectral with state-dependent coefficient optimization algorithm proposed solve defect. By introducing method, original problem transformed in...

In this letter, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving sequence of linear programs, resulting affine upper and lower hyperplanes with expanding operating regions. Although the problem can be solved using single program, existing approaches suffer from computation space complexity that grows exponentially s...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

‎in this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex banach space‎. ‎the results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...

Decomposing unitaries into a sequence of elementary operations is at the core of quantum computing. Information theoretic arguments show that approximating a random unitary with precision ε requires Ω(log(1/ε)) gates. Prior to our work, the state of the art in approximating a single qubit unitary included the Solovay-Kitaev algorithm that requires O(log(3+δ)(1/ε)) gates and does not use ancilla...

Measuring inconsistency in knowledge bases has been recognized as an important problem in several research areas. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. However, existing methods suffer from two limitations: 1) They are mostly restricted to propositional knowledge bases; 2) Very few of them discuss comput...

We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the theoretical work of [FK15b] with explicit algorithms and experiments with an implementation. More formally, the robustness of zero of a continuous map f : X → R is the maximal r > 0 such that each g : X → R with ‖f − g‖∞ ≤ r has a zero. We develop and implement an algorithm ap...