Continuous piecewise linear models constitute useful tools to extract the basic features about the patterns of growth in complex time series data. In this work, we present an iterative algorithm for continuous piecewise regression with automatic change-points estimation. The algorithm requires an initial guess about the number and positions of the change-points or hinges, which can be obtained ...

Space-time finite element methods for dynamic frictional contact problems are discussed in this article. The discretization scheme is based on a mixed formulation of the continuous problem, where the Lagrange multipliers represent the contact and frictional stresses. Using piecewise d-linear and globally continuous basis functions in space and time to construct the trial space for the displacem...

We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the constraints to be satisfied only at selected number points as in collocation, new approach alternates between minimizing constraining squared norm constraint residuals integrated along whole trajectories. As result, can obtain solutions higher ...

A class of piecewise continuous, piecewise C transformations on the interval [O, l] is shown to have absolutely continuous invariant measures.

A continuous system can be though of as a hybrid automaton with: Assumption 1 u and d are piecewise continuous functions of time. Remarks: The trivial dependence on q will be dropped from now on. Strictly speaking execution takes place over a hybrid time trajectory of the form 0 ; 0 0 ]] 1 ; 0 1 ] : : : , where u and d are continuous over each interval (refer to lecture 8). Notice that x() is c...

We shall consider slightly more general problems. Namely, we shall investigate the existence of continuous: piecewise monotone, piecewise strictly monotone, and piecewise linear n-th roots of interval maps which have a continuous n-th root. Here by an n-th root of f we mean a map g such that f = g (g is the n-th iterate of g). A continuous map f : I → J , where I, J are closed intervals, is pie...