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In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. [citation needed] Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation. [1] Divided differences is a recursive division process.
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.
A spreadsheet's concatenation ("&") function can be used to assemble complex text strings in a single cell (in this example, XML code for an SVG "circle" element). This concatenation is a variation of the chaining of formulas, for which spreadsheets are commonly used. The ability to chain formulas together is what gives a spreadsheet its power.
Excel offers many user interface tweaks over the earliest electronic spreadsheets; however, the essence remains the same as in the original spreadsheet software, VisiCalc: the program displays cells organized in rows and columns, and each cell may contain data or a formula, with relative or absolute references to other cells.
For that purpose, the divided-difference formula and/or its x 0 point should be chosen so that the formula will use, for its linear term, the two data points between which the linear interpolation of interest would be done. The divided difference formulas are more versatile, useful in more kinds of problems.
Let be the Lagrange interpolation polynomial for f at x 0, ..., x n.Then it follows from the Newton form of that the highest order term of is [, …,].. Let be the remainder of the interpolation, defined by =.
Cases of norovirus — the virulent, wildly contagious virus that causes vomiting and diarrhea — are increasing in the U.S., the Centers for Disease Control says, reporting double the amount of ...
Three-dimensional plot showing the values of the logarithmic mean. In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineering problems involving heat and mass transfer.