eft-horner

▸ function EFTHorner (p: number[], x: number): object

Defined in evaluate/double/eft-horner.ts:28

Returns an EFT (error free transformation) for the Horner evaluation of a polymial at a specified x. The result is returned as an object with properties: r̂ -> the calculated evaluation, pπ and pσ -> two polynomials with coefficients around 2^53 times smaller than the input polynomial.

• r̂ + pπ(x) + pσ(x) = the exact evaluation (no error)

• see Algorithms for Accurate, Validated and Fast Polynomial Evaluation, Stef Graillat, Philippe Langlois and Nicolas Louvet

• see also Philippe Langlois, Nicolas Louvet. Faithful Polynomial Evaluation with Compensated Horner Algorithm. ARITH18: 18th IEEE International Symposium on Computer Arithmetic, Jun 2007, Montpellier, France. pp.141–149. ffhal-00107222f

• see also Horner's Method

Parameters:

Name	Type	Description
p	number[]	a polynomial with coefficients given densely as an array of double floating point numbers from highest to lowest power, e.g. [5,-3,0] represents the polynomial 5x^2 - 3x
x	number	the value at which to evaluate the polynomial

Returns: object

Name	Type
r̂	number
pπ	number[]
pσ	number[]