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2. Piecewise function - Wikipedia

   en.wikipedia.org/wiki/Piecewise_function

   Terms like piecewise linear, piecewise smooth, piecewise continuous, and others are very common. The meaning of a function being piecewise P {\displaystyle P} , for a property P {\displaystyle P} is roughly that the domain of the function can be partitioned into pieces on which the property P {\displaystyle P} holds, but is used slightly ...

3. Piecewise linear function - Wikipedia

   en.wikipedia.org/wiki/Piecewise_linear_function

   Since the graph of an affine(*) function is a line, the graph of a piecewise linear function consists of line segments and rays. The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots.

4. Piecewise property - Wikipedia

   en.wikipedia.org/wiki/Piecewise_property

   A function property holds piecewise for a function, if the function can be piecewise-defined in a way that the property holds for every subdomain. Examples of functions with such piecewise properties are: Piecewise constant function, also known as a step function; Piecewise linear function; Piecewise continuous function

5. Linear interpolation - Wikipedia

   en.wikipedia.org/wiki/Linear_interpolation

   Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.

6. Word problem (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics)

   The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]

7. Spline (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Spline_(mathematics)

   In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

8. Pasting lemma - Wikipedia

   en.wikipedia.org/wiki/Pasting_lemma

   In topology, the pasting or gluing lemma, and sometimes the gluing rule, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions .

9. Segmented regression - Wikipedia

   en.wikipedia.org/wiki/Segmented_regression

   Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various ...