数値微分積分について
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概要
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In the study of the numerical calculation and integration an interesting part is a relation of Newton's interpolation formula to the numerical calculation. Namely. let D be a differential operator and Δ a difference operator. Then, for any function f∈C^ω(a, b), the following equations f(x+ph)=Σ^^∞__<r=0>([numerical formula])Δ^rf(x) specially hDf(x)=Σ∞^^__<r=1>(-1)^<r-1>1/rΔ^rf(x) are formed, where C^ω(a, b) is a class of analytic function in [a, b] and ([numerical formula])=p(p-1)(p-2)……(p-r+1)/r!. It is the object of this paper that lead to Newton's formula by the operational calculus, and numerical calculation and integration are treated consistenty from these relations. Further-more, we denote that the fundamental particularity of this method is shown from the proceeding of our considerations.
- 岐阜工業高等専門学校の論文
- 1973-03-15
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