produce twice as many digits of the final quotient on each iteration. Newton–Raphson and Goldschmidt algorithms fall into this category. Variants of these...

numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm...

A notable exception is Newton–Raphson division, which is independent from any numeral system. The term "Euclidean division" was introduced during the...

all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle...

as the highest position). This can in turn be used to implement Newton–Raphson division, perform integer to floating point conversion in software, and...

Restoring division Non-restoring division SRT division Newton–Raphson division: uses Newton's method to find the reciprocal of D, and multiply that reciprocal...

Restoring division Non-restoring division SRT division Newton–Raphson division: uses Newton's method to find the reciprocal of D, and multiply that reciprocal...

Trial division is the most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests...

In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

after some iterations. This practice happens to be the same as that of Newton–Raphson method, but with a completely different perspective. Neither he nor...

trial division by small primes) is performed first to improve performance. GMP since version 3.0 uses a base-210 Fermat test after trial division and before...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

finding its kth power as an integer and then finding the remainder after division by p. When the numbers involved are large, it is more efficient to reduce...

< (a,n) < n for all a ≤ r. It can be seen this is equivalent to trial division up to r, which can be done very efficiently without using gcd. Similarly...

numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder) of a by b. Denoting this remainder as a mod...

It is still used in some areas. The second Egyptian multiplication and division technique was known from the hieratic Moscow and Rhind Mathematical Papyri...

\operatorname {isqrt} (n)} is to use Heron's method, which is a special case of Newton's method, to find a solution for the equation x 2 − n = 0 {\displaystyle...

arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm...

tests instead of primality tests. The simplest primality test is trial division: given an input number, n {\displaystyle n} , check whether it is divisible...

may be solved with rapid convergence (but slow near the poles) using Newton–Raphson iteration: θ 0 = φ , θ n + 1 = θ n − 2 θ n + sin ⁡ 2 θ n − π sin ⁡ φ...

of polynomials, described by Horner in 1819. It is a variant of the Newton–Raphson method made more efficient for hand calculation by application of Horner's...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

method might be even slower than trial division (worst case). Nonetheless, the combination of trial division and Fermat's is more effective than either...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

Schönhage–Strassen Fürer's Euclidean division Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT Discrete logarithm Baby-step giant-step Pollard rho Pollard...

it applies. Between them, one can consider: root finding (using e.g. Newton-Raphson method) system of linear equations (using e.g. LU decomposition) ordinary...