Interpolation: Second EditionCourier Corporation, 7 нояб. 2013 г. - Всего страниц: 272 In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines" in a set of tables by constructing new data points from existing points. This rigorous presentation employs only formulas for which it is possible to calculate error limits. Subjects include displacement symbols and differences, divided differences, formulas of interpolation, factorial coefficients, numerical differentiation, and construction of tables. Additional topics include inverse interpolation, elementary methods of summation, repeated summation, mechanical quadrature, numerical integration of differential equations, the calculus of symbols, interpolation with several variables, and mechanical cubature. 1950 edition. |
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a₁ arguments arithmetical means B₁ B₂ B₂r Bernoulli's polynomials Bessel's formula calculation central differences change its sign column constant decimals denoting derived difference-table differential coefficients displacement-symbols divided differences equation error Error-Test Everett's expansion expression f(ao f(xo function function-table Gaussian formula given values identical insert instance integral interpolation-formula interval Lagrange's formula Laplace's formula linear linear function Lubbock's Mean Value method multiplying Newton's formula number of terms numerical integration obtain open type order 2k polynomial of degree practical proved put f(x remainder-term result Rolle's theorem seen Stirling's formula summation summation-formula symbol t)dt Theorem of Mean theory of interpolation thereafter tion values of f(x vanish variables whence write written x(x² Xn+1 α α Σ Δ Σ Σ Σχ