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Some languages do not offer string interpolation, instead using concatenation, simple formatting functions, or template libraries. String interpolation is common in many programming languages which make heavy use of string representations of data, such as Apache Groovy, Julia, Kotlin, Perl, PHP, Python, Ruby, Scala, Swift, Tcl and most Unix shells.
One of the oldest examples is in shell scripts, where single quotes indicate a raw string or "literal string", while double quotes have escape sequences and variable interpolation. For example, in Python, raw strings are preceded by an r or R – compare 'C:\\Windows' with r'C:\Windows' (though, a Python raw string cannot end in an odd number ...
Polynomial interpolation can estimate local maxima and minima that are outside the range of the samples, unlike linear interpolation. For example, the interpolant above has a local maximum at x ≈ 1.566, f(x) ≈ 1.003 and a local minimum at x ≈ 4.708, f(x) ≈ −1.003.
In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid.
Simpson's 1/3 rule, also simply called Simpson's rule, is a method for numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for =.
Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions.
Polynomial interpolation also forms the basis for algorithms in numerical quadrature (Simpson's rule) and numerical ordinary differential equations (multigrid methods). In computer graphics, polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography.
A ninth order polynomial interpolation (exact replication of the red curve at 10 points) In the mathematical field of numerical analysis , Runge's phenomenon ( German: [ˈʁʊŋə] ) is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced ...