The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion Bo Li, Yuanguo Zhu & Yuefen Chen To cite this article: Bo Li, Yuanguo Zhu & Yuefen Chen (2017) The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion, International Journal of Systems Science, 48:8, 1766-1774, DO...

The NNM (Nonlinear normal modes) have recently been investigated with the method of strained coordinates for spring mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expan...

Pruned tree-structured scalar quantizers are a form of non-uniform scalar quantizer that are named due to being designed via pruning a tree-structured scalar quantizer [1]. If designed via pruning a uniform tree-structured scalar quantizer, such a quantizer may be mapped to a piecewise linear compandor. An algorithm has been developed for mapping a piecewise linear compandor onto a a tree-struc...

Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...

A robust optimal-order multigrid method for the pure traction problem in two-dimensional linear elasticity is studied. The finite element discretization is a variant of a mixed method proposed by Falk where the displacement is approximated by nonconforming piecewise linear functions and the "pressure" is approximated by piecewise constant functions on a coarser grid. Full multigrid convergence ...

A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fitting C1 piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examp...

The paper deals with a problem of linearization of multi-output logic functions. Specifically, the case is discussed, when the functions have a large number of variables and cannot be efficiently linearized by using known techniques. For solution of the problem a socalled piecewise linearization is proposed. The piecewise linearization comprises decomposition of an initial multi-output function...

Consider a piecewise smooth function for which the (pseudo-)spectral coefficients are given. It is well known that while spectral partial sums yield exponentially convergent approximations for smooth functions, the results for piecewise smooth functions are poor, with spurious oscillations developing near the discontinuities and a much reduced overall convergence rate. This behavior, known as t...

Osteoporosis is a disease in which low bone mass and microarchitectural deterioration of bone tissue lead to increased bone fragility and a consequent increase in fracture risk. The objective of this paper is to develop and validate a new method to assess bone microarchitecture on radiographs. Taking into account the piecewise fractal nature of bone radiograph images, an appropriate fractal mod...

In this paper, an adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity. Whenever for some s > 0, the solution can be approximated to accuracy O(n−s) in energy norm by a continuous piecewise linear function on some partition with n triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate ...