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Nutshell tables of mathematical functions for interpolation with calculating machines
Summary Taylor Tables of Functions.The numerical values to ten decimal places of simple functions can be obtained from tables that cover only one page if a curvilinear interpolation will be applied, in a striking contrast to the familiar logaritmic and trigonometric thesauri which fill hundreds of pages. Only the interpolation formula must be adapted in a form convenient for calculating machines and the usual schema of differences replaced by a set of coefficients A, B, C... proportional to the higher derivatives. The formula reads as (3), where the constant multiplier ±t<1 once for all can be put into the keyboard of the machine.The table can be prepared very rapidly for any function of one variable (excepting, of course, those with short period disturbances). The coefficients can be computed by the aid of formulas (2), if the higher derivatives have simple mathematical expressions. In the other cases the coefficients can be obtained from the usual schema of differencesD using the formulas (4), or from the values of the function itself using the auxiliary table above the check formula (6).The tables can be used for numerical differentiations and integrations too. At last practical tables to ten decimal places of logarithms, antilogarithms and main trigonometric functions are given.Tables for the Computation of Long Geodetic Lines.The method ofLevallois andDupuy (Bull. géod. no 16) for the computation of long geodetic lines can be simplified by some special tables, which are given here. These tables can be made very concise using the idea of the author explained in a previous article (Bull. géod. no 29, p. 269). The accuracy of the method meets the highest demands of the present practical geodesy, and, neglecting the last decimal places, any degree of approximation can be obtained most economically.
Nutshell tables of mathematical functions for interpolation with calculating machines
Summary Taylor Tables of Functions.The numerical values to ten decimal places of simple functions can be obtained from tables that cover only one page if a curvilinear interpolation will be applied, in a striking contrast to the familiar logaritmic and trigonometric thesauri which fill hundreds of pages. Only the interpolation formula must be adapted in a form convenient for calculating machines and the usual schema of differences replaced by a set of coefficients A, B, C... proportional to the higher derivatives. The formula reads as (3), where the constant multiplier ±t<1 once for all can be put into the keyboard of the machine.The table can be prepared very rapidly for any function of one variable (excepting, of course, those with short period disturbances). The coefficients can be computed by the aid of formulas (2), if the higher derivatives have simple mathematical expressions. In the other cases the coefficients can be obtained from the usual schema of differencesD using the formulas (4), or from the values of the function itself using the auxiliary table above the check formula (6).The tables can be used for numerical differentiations and integrations too. At last practical tables to ten decimal places of logarithms, antilogarithms and main trigonometric functions are given.Tables for the Computation of Long Geodetic Lines.The method ofLevallois andDupuy (Bull. géod. no 16) for the computation of long geodetic lines can be simplified by some special tables, which are given here. These tables can be made very concise using the idea of the author explained in a previous article (Bull. géod. no 29, p. 269). The accuracy of the method meets the highest demands of the present practical geodesy, and, neglecting the last decimal places, any degree of approximation can be obtained most economically.
Nutshell tables of mathematical functions for interpolation with calculating machines
Hirvonen, R. A. (Autor:in)
1953
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Geodäsie , Geometrie , Geodynamik , Mathematik , Mineralogie
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