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The secant method can be interpreted as a method in which the derivative is replaced by an approximation and is thus a quasi-Newton method. If we compare Newton's method with the secant method, we see that Newton's method converges faster (order 2 against order the golden ratio φ ≈ 1.6). [ 2 ]
The saddlepoint approximation method, initially proposed by Daniels (1954) [1] is a specific example of the mathematical saddlepoint technique applied to statistics, in particular to the distribution of the sum of independent random variables.
Rational approximation may refer to: Diophantine approximation , the approximation of real numbers by rational numbers Padé approximation , the approximation of functions obtained by set of Padé approximants
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
There is an intimate connection between regular continued fractions and Padé tables with normal approximants along the main diagonal: the "stairstep" sequence of Padé approximants R 0,0, R 1,0, R 1,1, R 2,1, R 2,2, ... is normal if and only if that sequence coincides with the successive convergents of a regular continued fraction.
Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros are simple, which means that there is no multiplicity in poles and zeros.
A mollifier (top) in dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version. In mathematics, mollifiers (also known as approximations to the identity) are particular smooth functions, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via ...
Illustration of numerical integration for the equation ′ =, = Blue: the Euler method, green: the midpoint method, red: the exact solution, =. The step size is = The same illustration for =