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Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
For example, we might want to calculate the relative change of −10 to −6. The above formula gives (−6) − (−10) / −10 = 4 / −10 = −0.4, indicating a decrease, yet in fact the reading increased. Measures of relative change are unitless numbers expressed as a fraction. Corresponding values of percent change would be ...
Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.
Unweighted, or "elementary", price indices only compare prices of a single type of good between two periods. They do not make any use of quantities or expenditure weights. They are called "elementary" because they are often used at the lower levels of aggregation for more comprehensive price indices. [2]
The normalized angle, referred to as angular distance, between any two vectors and is a formal distance metric and can be calculated from the cosine similarity. [5] The complement of the angular distance metric can then be used to define angular similarity function bounded between 0 and 1, inclusive.
The key feature of spreadsheets is the ability for a formula to refer to the contents of other cells, which may, in turn, be the result of a formula. To make such a formula, one replaces a number with a cell reference. For instance, the formula =5*C10 would produce the
The magenta line shows that the harmonic mean of 6 and −2 is −6. The red line shows that the harmonic mean of a number and its negative is undefined as the line does not intersect the z axis. For the special case of just two numbers, and , the harmonic mean can be written as: [4]