Results 211 to 220 of about 6,069,876 (245)

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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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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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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Multivariate Divided Differences with Simple Knots

SIAM Journal on Numerical Analysis, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Leibniz Formula for Multivariate Divided Differences

SIAM Journal on Numerical Analysis, 2003
In this paper, the algebraic background of the Leibniz formula is explored, showing the formula to be equivalent to the Opitz formula [\textit{G. Opitz}, Z. Angew. Math. Mech. 44, Sonderheft, T52--T54 (1964; Zbl 0196.48801)] that gives the divided difference table of any polynomial as the result of applying that polynomial to a certain matrix. This, in
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Dividing on a Different Schedule

Science's STKE, 2006
Some multinucleated cells progress through the cell cycle synchronously, and the linear progression occurs by regulated degradation of cyclins, just as in mononucleated cells. However, there are other examples where the nuclei undergo asynchronous divisions. Gladfelter et al.
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A Remark on Divided Differences

The American Mathematical Monthly, 1989
(1989). A Remark on Divided Differences. The American Mathematical Monthly: Vol. 96, No. 7, pp. 618-622.
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Interpolation and divided differences

2002
Abstract The problem that we consider in this chapter is the following: let f be a function which we assume to be continuous on the interval [a, b] and let xO, xl,... , xn be n + 1 pairwise distinct points given in the interval [a, b].
Michelle Schatzman, John Taylor
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A functional equation related to divided differences

Lithuanian Mathematical Journal, 1977
where [~(z); z~: . . 9 ~m] denote the m-th-order divided difference [i] of the function o~i:)~SIE and ao, al, ., an are complex constants. The operator (i) is defined for those functions o~(--)~=S(E) which do not assume the value infinity at the points ~, ~2, ~nIt is obviously linear 9 We call it the n-th order linear divided-difference operator. Let U(
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