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A Divided Difference Expansion of a Divided Difference
"... A divided difference expansion with remainder for a general divided difference is derived that contains Floater's recent derivative expansion as a special case. ..."
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A divided difference expansion with remainder for a general divided difference is derived that contains Floater's recent derivative expansion as a special case.
running head: DIVIDED DIFFERENCE EXPANSION OF DIVIDED DIFFERENCE
"... 1 Abstract A divided difference expansion with remainder for a general divided difference is derived that contains Floater’s recent derivative expansion as a special case. key words divided difference, univariate, remainder, interpolation 2 It is the purpose of this note to record a divided differen ..."
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1 Abstract A divided difference expansion with remainder for a general divided difference is derived that contains Floater’s recent derivative expansion as a special case. key words divided difference, univariate, remainder, interpolation 2 It is the purpose of this note to record a divided
DIVIDED DIFFERENCES OF IMPLICIT FUNCTIONS
, 2010
"... Under general conditions, the equation g(x,y) = 0 implicitly defines y locally as a function of x. In this article, we express divided differences of y in terms of bivariate divided differences of g, generalizing a recent result on divided differences of inverse functions. ..."
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Cited by 1 (1 self)
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Under general conditions, the equation g(x,y) = 0 implicitly defines y locally as a function of x. In this article, we express divided differences of y in terms of bivariate divided differences of g, generalizing a recent result on divided differences of inverse functions.
An Efficient Definition of the Divided Difference
"... Dedicated to Borislav Bojanov on the occasion of his sixtieth birthday A novel definition of the divided difference is shown to lead most readily to the standard basic properties of the divided difference. 1. ..."
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Dedicated to Borislav Bojanov on the occasion of his sixtieth birthday A novel definition of the divided difference is shown to lead most readily to the standard basic properties of the divided difference. 1.
Symbolic Computation of Divided Differences
, 1999
"... Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x) - f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulati ..."
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Cited by 4 (1 self)
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Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x) - f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference
A multivariate divided differences
- Approximation Theory VIII
, 1995
"... “Est enim fere ex pulcherrimis quæ solvere desiderem.” (It is among the most beautiful I could desire to solve.) [Newton 1676] Abstract. Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) ..."
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Cited by 19 (0 self)
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“Est enim fere ex pulcherrimis quæ solvere desiderem.” (It is among the most beautiful I could desire to solve.) [Newton 1676] Abstract. Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate)
AN INEQUALITY FOR DIVIDED DIFFERENCES IN HIGH DIMENSIONS
"... ABSTRACT. This paper is devoted to an inequality for divided differences in the multivariate case which is similar to the inequality obtained by [J. Pečarić, and M. Rodić Lipanović, On an inequality for divided differences, Asian-European Journal of Mathematics, Vol. 1, No. 1 (2008), 113-120]. Key w ..."
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ABSTRACT. This paper is devoted to an inequality for divided differences in the multivariate case which is similar to the inequality obtained by [J. Pečarić, and M. Rodić Lipanović, On an inequality for divided differences, Asian-European Journal of Mathematics, Vol. 1, No. 1 (2008), 113-120]. Key
Connection-Matrix Splines by Divided Differences
, 1996
"... We move the classical, divided-difference construction for B-splines into a connection-matrix setting by establishing a one-sided basis for connection-matrix splines together with a differencing process that transforms the one-sided basis into a compact-support basis that partitions unity. ..."
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We move the classical, divided-difference construction for B-splines into a connection-matrix setting by establishing a one-sided basis for connection-matrix splines together with a differencing process that transforms the one-sided basis into a compact-support basis that partitions unity.
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