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In univariate interpolation, an interpolant is a function L=L(x) which agrees with a particular function f at a set of known points x_0,x_1,x_2,...,x_n and which is used to ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

A method for finding roots which defines P_j(x)=(P(x))/((x-x_1)...(x-x_j)), (1) so the derivative is (2) One step of Newton's method can then be written as ...

Formulas obtained from differentiating Newton's forward difference formula, where R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi), (n; k) is a ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly ...

An integer-relation algorithm which is based on a partial sum of squares approach, from which the algorithm takes its name.

Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...