Lossy compression schemes are often desirable in many signal processing applications such as the compression of ECG data. This paper presents a relaxation of a provably good algorithm for lossy signal compression, bas...
详细信息
Lossy compression schemes are often desirable in many signal processing applications such as the compression of ECG data. This paper presents a relaxation of a provably good algorithm for lossy signal compression, based on the piecewiselinear approximation of functions. The algorithm approximates the data within a given tolerance using a piecewise linear function. The paper also describes an architecture suitable for the single-chip implementation of the proposed algorithm. The design consists of control, two multiply/divide units, four adder/subtracter units, and an I/0 interface unit. For uniformly sampled data, no division is required, and all operations can be completed in a pipelined manner in at most three cycles per sample point. The corresponding simplified architecture is also presented.
In this paper the problem of the partition of a polygon Ω into quadrilaterals (quadrangles and triangles) is studied, for which four given boundary pointsA i (1⩽i⩽4) become the vertices of a quadrilateral, and the pa...
详细信息
In this paper the problem of the partition of a polygon Ω into quadrilaterals (quadrangles and triangles) is studied, for which four given boundary pointsA i (1⩽i⩽4) become the vertices of a quadrilateral, and the partition itself is topologically equivalent to a special partition of a rectangle Q into rectangles with sides parallel to the sides of Q. This problem is closely connected with the problem of choosing a basis of piecewise linear functions in the projective-difference method, for which the projective-difference analog of the operator -Δ ≡-(∂2/∂x2 + ∂2/∂y2) for a boundary-value problem in Ω turns out to be spectrally equivalent to its simplest difference analog in a rectangle (see [1–5]).
The task of finding global optima to general classes of nonconvex optimization problem is attracting increasing attention. McCormick [4] points out that many such problems can conveniently be expressed in separable fo...
详细信息
The task of finding global optima to general classes of nonconvex optimization problem is attracting increasing attention. McCormick [4] points out that many such problems can conveniently be expressed in separable form, when they can be tackled by the special methods of Falk and Soland [2] or Soland [6], or by Special Ordered Sets. Special Ordered Sets, introduced by Beale and Tomlin [1], have lived up to their early promise of being useful for a wide range of practical problems. Forrest, Hirst and Tomlin [3] show how they have benefitted from the vast improvements in branch and bound integer programming capabilities over the last few years, as a result of being incorporated in a general mathematical programming ***, Special Ordered Sets in their original form require that any continuous functions arising in the problem be approximated by piecewise linear functions at the start of the analysis. The motivation for the new work described in this paper is the relaxation of this requirement by allowing automatic interpolation of additional relevant points in the course of the *** is similar to an interpolation scheme as used in separable programming, but its incorporation in a branch and bound method for global optimization is not entirely straightforward. Two by-products of the work are of interest. One is an improved branching strategy for general special-ordered-set problems. The other is a method for finding a global minimum of a function of a scalar variable in a finite interval, assuming that one can calculate function values and first derivatives, and also bounds on the second derivatives within any *** paper describes these methods, their implementation in the UMPIRE system, and preliminary computational experience.
A repeated scanning algorithm for determining the minimax approximation to an arbitrary function by means of a piecewise linear function with a fixed number of variable knots is described, and it is compared to optima...
详细信息
A repeated scanning algorithm for determining the minimax approximation to an arbitrary function by means of a piecewise linear function with a fixed number of variable knots is described, and it is compared to optimal and suboptimal methods.
Convergence of the finite element solutionuh of the Dirichlet problem Δu=δ is proved, where δ is the Dirac δ-function (unit impulse). In two dimensions, the Green's function (fundamental solution)u lies outsid...
详细信息
Convergence of the finite element solutionuh of the Dirichlet problem Δu=δ is proved, where δ is the Dirac δ-function (unit impulse). In two dimensions, the Green's function (fundamental solution)u lies outsideH1, but we are able to prove that\(\parallel u - u^h \parallel _{L^2 } = O (h)\). Since the singularity ofu is logarithmic, we conclude that in two dimensions the function log γ can be approximated inL2 near the origin by piecewise linear functions with an errorO (h). We also consider the Dirichlet problem Δu=f, wheref is piecewise smooth but discontinuous along some curve. In this case,u just fails to be inH5/2, but as with the approximation to the Green's function, we prove the full rate of convergence:‖u−uh‖1=O (h8/2) with, say, piecewise quadratics.
暂无评论