Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Energy-momentum conservation for gravitational two-body scattering in the post-linear approximation

Abstract: The equations of motion for the gravitational scattering of two point masses obtained in a post-linear approximation to general relativity are integrated by iteration starting with uniform straight-line motion. The ensuing conservation laws for energy and linear momentum disprove Rosenblum's recent claim of an energy loss in a post-linear approximation scheme.

Are bilinear quadrilaterals better than linear triangles

Abstract: This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. The theory and numerical results suggest triangles may have a slight advantage over quadrilaterals for interpolating convex data function but bilinear approximation may offer a higher order approximation for saddle-shaped functions on a well-designed mesh. This work is a basic study on optimal meshes with the intention of gaining insight into the more complex meshing problems in finite element analysis.

Multidimensional linear distinguishing attacks and Boolean functions

Abstract: Linear cryptanalysis and linear approximation methods in general are among the most important cryptanalysis methods of symmetric ciphers and their components. Recently, these methods have been extended to efficiently exploit multiple linear approximations simultaneously. It is known that high nonlinearity of Boolean functions and S-boxes is a desirable property and that the bent functions offer the strongest resistance against cryptanalysis using single linear approximations. The goal of this paper is to investigate to which extent resistance against the multidimensional extension of the linear cryptanalysis method can be achieved. For this purpose some common highly nonlinear Boolean functions as well as a basic LFSR based key stream generator using a nonlinear filter function are investigated.

Quadratically Constrained Quadratic-Programming Based Control of Legged Robots Subject to Nonlinear Friction Cone and Switching Constraints

Abstract: A hierarchical control architecture is presented for energy-efficient control of robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation limits, and yet minimizing the power losses in the joint actuators. The control formulation can incorporate the nonlinear friction cone constraints into the control without recourse to the common linear approximation of the constraints or introduction of slack variables. A performance metric is introduced that allows trading-off the multiple constraints when otherwise finding an optimal solution is not feasible. Moreover, the projection-based controller does not require the minimal-order dynamics model and hence allows switching contacts that are particularly appealing for legged or walking robots. The fundamental properties of constrained inertia matrix derived are similar to those of general inertia matrix of the system, and subsequently these properties are greatly exploited for control design purposes. The problem of task space control with minimum (point-wise) power dissipation subject to all physical constraints is transcribed into a quadratically constrained quadratic programming that can be solved by barrier methods. Experimental results are appended to comparatively demonstrate the efficiency and performance of the optimal controller.