Piecewise

Piecewise-linear approximation Software such as the PLECS interface to Simulink uses piecewise-linear approximation of the equations governing the elements of a circuit.

Piecewise linear approximation to exponential and logarithm Integers reinterpreted as floating point numbers (in blue, piecewise linear), compared to a scaled and shifted logarithm (in gray, smooth).

Relationship to piecewise/composite Bézier A piecewise/composite Bézier curve is a series of Bézier curves joined with at least C0 continuity (the last point of one curve coincides with the starting point of the next curve).

Ninth-grade student Rosemary Madu showed attendees how she created an Easter bunny on a graph using piecewise functions.

Among other things, he showed that every piecewise continuous function is integrable.

Basic radiosity also has trouble resolving sudden changes in visibility (e.g. hard-edged shadows) because coarse, regular discretization into piecewise constant elements corresponds to a low-pass box filter of the spatial domain.

Conversely, given a real number, if one takes the floating point representation and considers it as an integer, one gets a piecewise linear approximation of a shifted and scaled base 2 logarithm, (hence actually ), as shown at right.

Dirichlet has shown this for continuous, piecewise-differentiable functions (thus with countably many non-differentiable points).

Expressions for the polynomial pieces can be derived by means of the Cox-de Boor recursion formula de Boor, p 131. : : de Boor, p. 131 That is, is piecewise constant one or zero indicating which knot span x is in (zero if knot span j is repeated).

For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable.

HMMs are used in speech recognition because a speech signal can be viewed as a piecewise stationary signal or a short-time stationary signal.

In more complex cases the circuit may be analyzed with specialized computer programs or estimation techniques such as the piecewise-linear model.

Integration of the beam equation again results in piecewise polynomial deflection.

Nonlinear dynamical systems and chaos main Simple nonlinear dynamical systems and even piecewise linear systems can exhibit a completely unpredictable behavior, which might seem to be random, despite the fact that they are fundamentally deterministic.

Simpson's rule approximates the integrand by a piecewise quadratic function.

The logistic map is only a second-degree polynomial; the horseshoe map is piecewise linear.

These properties uniquely characterize surface area for a wide class of geometric surfaces called piecewise smooth.

This simplifies finding a start value for the iterative method that is close to the square root, for which a polynomial or piecewise-linear approximation can be used.