Results 201 to 210 of about 1,836,288 (255)

Polynomials and divided differences

Publicationes Mathematicae Debrecen, 2005
\textit{J. Aczél} showed in 1963 [see Math. Mag. 58, 42--45 (1985; Zbl 0571.39005)] that there is a simple functional equation involving two unknown functions, say \(f\) and \(g\), whose general solution (no regularity conditions whatever) is: \(f\) is a polynomial of degree at most 2 and \(g\) is the derivative of \(f\).
Riedel, Thomas, Sablik, Maciej, Sklar, Abe   +2 more
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Interlacing zeros and divided differences

Russian Mathematical Surveys, 2004
The communication under review deals with the construction of sequences which alternate or preserve its sign. Two theorems generalize well known facts as that stated for polynomials with real simple zeros for which the signs of the critical values alternate. Let \(H=\{h_1,\dots ,h_n\} \) be a complete Chebyshev system on the interval \(I\), and let \(X=
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Divided Differences and Combinatorial Identities

Studies in Applied Mathematics, 1991
We present an algebraic theory of divided differences which includes confluent differences, interpolation formulas, Liebniz's rule, the chain rule, and Lagrange inversion. Our approach uses only basic linear algebra. We also show that the general results about divided differences yield interesting combinatorial identities when we consider some suitable
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Root finding by divided differences

Numerische Mathematik, 1981
A recursive method is presented for computing a simple zero of an analytic functionf from information contained in a table of divided differences of its reciprocalh=1/f. A good deal of flexibility is permitted in the choice of ordinate and derivative values, and in the choice of the number of previous points upon which to base the next estimate of the ...
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