113. A new interpolation
If we wish to interpolate values of a function between two given values y1, and y2, we may employ a polynomial in x1. When the only conditions to be satisfied are that the function take the value y1 when x=l, and the value y2 when x=2, the polynomial of minimum degree is of the form a0+a1 (x-1). Interpolation by means of this polynomial is that ordinarily employed when using trigonometric and logarithmic tables, and is spoken of as interpolation by first differences. If, however, additional conditions are imposed the degree of the polynomial will increase one unit for each condition. For example, if the interpolated values between y1 and y2 are dependent upon the conditions that the function takes the value y0 when x=0, and the value y3 when x=3, then the interpolation polynomial is of the form a0+a1 (x-1) + a2 (x-1)2 + a3 (x-1)3.
Proceedings of the Iowa Academy of Science
©1924 Iowa Academy of Science, Inc.
Reilly, John F.
"A New Interpolation Formula,"
Proceedings of the Iowa Academy of Science, 31(1), 369-371.
Available at: https://scholarworks.uni.edu/pias/vol31/iss1/114