Topic
Piecewise linear function
About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.
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TL;DR: This paper introduces a method to reduce the complexity by relaxing the demand for optimality, which is applied to a partially observable Markov decision problem (POMDP).
Abstract: The idea of dynamic programming is general and very simple, but the "curse of dimensionality" is often prohibitive and restricts the fields of application. This paper introduces a method to reduce the complexity by relaxing the demand for optimality. The distance from optimality is kept within prespecified bounds and the size of the bounds determines the computational complexity. Several computational examples are considered. The first is optimal switching between linear systems, with application to design of a dc/dc voltage converter. The second is optimal control of a linear system with piecewise linear cost with application to stock order control. Finally, the method is applied to a partially observable Markov decision problem (POMDP)
311 citations
TL;DR: Algorithm for constructing a hierarchy of increasingly coarse Morse—Smale complexes that decompose a piecewise linear 2-manifold by canceling pairs of critical points in order of increasing persistence is presented.
Abstract: . We present algorithms for constructing a hierarchy of increasingly coarse Morse—Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse—Smale complexes by canceling pairs of critical points in order of increasing persistence.
307 citations
TL;DR: In this article, a volume-of-fluid scheme with piecewise linear interface construction is proposed to implement the contact angle condition, where the body forces are treated as a continuous body force, computed from numerical derivatives of a smoothed volume of fluid function.
302 citations
TL;DR: A new approach to determination of mapping functions for registration of digital images is presented, where the images are divided into triangular regions by triangulating the control points and the overall mapping function is obtained by piecing together the linear mapping functions.
297 citations
TL;DR: In this paper, an iterative sensitivity based finite element (FE) model updating method is proposed, in which the discrepancies in both the eigenfrequencies and unscaled mode shape data obtained from ambient tests are minimized.
294 citations