Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers

Abstract: A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Coding for a binary independent piecewise-identically-distributed source

Abstract: Two weighting procedures are presented for compaction of output sequences generated by binary independent sources whose unknown parameter may occasionally change. The resulting codes need no knowledge of the sequence length T, i.e., they are strongly sequential, and also the number of parameter changes is unrestricted. The additional-transition redundancy of the first method was shown to achieve the Merhav lower bound, i.e., log T bits per transition. For the second method we could prove that additional-transition redundancy is not more than 3/2 log T bits per transition, which is more than the Merhav bound; however, the storage and computational complexity of this method are also more interesting than those of the first method. Simulations show that the difference in redundancy performance between the two methods is negligible.

Weak Galerkin Finite Element Methods on Polytopal Meshes

Abstract: This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed and why they provide reliable numerical approximations for the underlying partial differential equations. In particular, optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the WG-FEM. All the results are derived for finite element partitions with polytopes. Allowing the use of discontinuous approximating functions on arbitrary polytopal elements is a highly demanded feature for numerical algorithms in scientific computing.

Directional derivatives of the solution of a parametric nonlinear program

Abstract: Consider a parametric nonlinear optimization problem subject to equality and inequality constraints. Conditions under which a locally optimal solution exists and depends in a continuous way on the parameter are well known. We show, under the additional assumption of constant rank of the active constraint gradients, that the optimal solution is actually piecewise smooth, hence B-differentiable. We show, for the first time to our knowledge, a practical application of quadratic programming to calculate the directional derivative in the case when the optimal multipliers are not unique.

Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming

Abstract: A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and controls and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory that can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.