In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S. ) is either of two things: (i) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form; or (ii) a method for approximating the roots of a polynomial. The latter is also known as Ruffini–Horner's method. These methods are named after the British mathematician William George Horner, although they were known before him.
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Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x − x/4 + 7 is a polynomial, but x − 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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Arithmetic underflow
The term arithmetic underflow (or "floating point underflow", or just "underflow") is a condition in a computer program where the result of a calculation is a smaller number than what the computer can actually store in memory. Arithmetic underflow can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype.
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