Explore: Padé Approximation

Henri Padé, but goes back to Georg Frobenius, who introduced the idea and investigated the features of rational approximations of power series. The Padé approximant

Eugène Padé (French: [pade]; 17 December 1863 – 9 July 1953) was a French mathematician, who is now remembered mainly for his development of Padé approximation

Rational approximation may refer to: Diophantine approximation, the approximation of real numbers by rational numbers Padé approximation, the approximation of

the desired interval of approximation. Another approximation is given by Sergei Winitzki using his "global Padé approximations": erf ⁡ ( x ) ≈ sgn ⁡ x

y1 is a result of simulation of Padé approximation of 2nd order, y2 is a result of simulation of Padé approximation of 4th order and y3 is result of

s\in \mathbb {C} } is complex frequency. This can be approximated using a Padé approximant, as follows: e − s T = e − s T / 2 e s T / 2 ≈ 1 − s T / 2 1

Halley's method exactly finds the roots of a linear-over-linear Padé approximation to the function, in contrast to Newton's method or the Secant method

combine a polynomial or rational approximation (such as Chebyshev approximation, best uniform approximation, Padé approximation, and typically for higher or

the function f, the Padé approximation also has d + 1 coefficients dependent on f and its derivatives. More precisely, in any Padé approximant, the degrees

In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants Rm, n to a given complex formal power series