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Arbitrary precision arithmetic is also used to compute fundamental mathematical constants such as π to millions or more digits and to analyze the properties of the digit strings [8] or more generally to investigate the precise behaviour of functions such as the Riemann zeta function where certain questions are difficult to explore via ...
Routines for Gauss–Kronrod quadrature are provided by the QUADPACK library, the GNU Scientific Library, the NAG Numerical Libraries, R, [2] the C++ library Boost., [3] as well as the Julia package QuadGK.jl [4] (which can compute Gauss–Kronrod formulas to arbitrary precision).
This allows the calculation to run indefinitely varying the amount of intermediate storage as the calculation progresses. A variant of the spigot approach uses an algorithm which can be used to compute a single arbitrary digit of the transcendental without computing the preceding digits: an example is the Bailey–Borwein–Plouffe formula , a ...
Many transcendental equations can be solved up to an arbitrary precision by using Newton's method. For example, finding the cumulative probability density function, such as a Normal distribution to fit a known probability generally involves integral functions with no known means to solve in closed form. However, computing the derivatives needed ...
Bailey (2006) found that: "The Tanh-Sinh quadrature scheme is the fastest currently known high-precision quadrature scheme, particularly when one counts the time for computing abscissas and weights. It has been successfully employed for quadrature calculations of up to 20,000-digit precision."
In the 1980s, Rump made an example. [ 3 ] [ 4 ] He made a complicated function and tried to obtain its value. Single precision, double precision, extended precision results seemed to be correct, but its plus-minus sign was different from the true value.
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
dc: "Desktop Calculator" arbitrary-precision RPN calculator that comes standard on most Unix-like systems. KCalc, Linux based scientific calculator; Maxima: a computer algebra system which bignum integers are directly inherited from its implementation language Common Lisp. In addition, it supports arbitrary-precision floating-point numbers ...