interpolantn.

/ɪnˈtəːpələnt/

Etymology: < Latin interpolant-em, present participle of interpolāre (see interpolate v.), or interpol- (in interpolate v.) + -ant suffix¹.

Mathematics.

A value or expression (given or calculated) used in finding some other value by interpolation.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > used to calculate other value

interpolant1920

1920 Tracts for Computers ii. 17 Forward difference formulae, central difference formulae and Lagrangian formulae, when the interpolants are spaced equally apart are really different aspects of the same process, i.e. running a parabola of the (n–1)th order through n points.

1946 Philos. Mag. 37 260 A function value interpolated in this way may indeed be more accurate than any of the eight values used to obtain it. For in a perfect table the rounding-off errors of the eight interpolants have uniform probability distributions between − 0·5 and 0·5 in units of the last decimal, and it may be shown that the probability of the resulting error of the interpolate is very nearly normally distributed with standard deviation 0·12.

1965 A. Ralston First Course Numerical Anal. iii. 57 An important advantage of finite-difference interpolation formulas..would seem to be the property..that enables a term to be added to them merely by adding one tabular point and computing an additional row of differences... This enables us to generate a sequence of interpolants each involving one more tabular point than the previous one.

This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018).

单词	interpolant
释义	interpolantn. /ɪnˈtəːpələnt/ Etymology: < Latin interpolant-em, present participle of interpolāre (see interpolate v.), or interpol- (in interpolate v.) + -ant suffix¹. Mathematics. A value or expression (given or calculated) used in finding some other value by interpolation. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > used to calculate other value interpolant1920 1920 Tracts for Computers ii. 17 Forward difference formulae, central difference formulae and Lagrangian formulae, when the interpolants are spaced equally apart are really different aspects of the same process, i.e. running a parabola of the (n–1)th order through n points. 1946 Philos. Mag. 37 260 A function value interpolated in this way may indeed be more accurate than any of the eight values used to obtain it. For in a perfect table the rounding-off errors of the eight interpolants have uniform probability distributions between − 0·5 and 0·5 in units of the last decimal, and it may be shown that the probability of the resulting error of the interpolate is very nearly normally distributed with standard deviation 0·12. 1965 A. Ralston First Course Numerical Anal. iii. 57 An important advantage of finite-difference interpolation formulas..would seem to be the property..that enables a term to be added to them merely by adding one tabular point and computing an additional row of differences... This enables us to generate a sequence of interpolants each involving one more tabular point than the previous one. This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018). < n.1920
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