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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature ) is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals.
For the second iteration the values of the first iteration are used in the formula 16 × (more accurate) − (less accurate) / 15 The third iteration uses the next power of 4: 64 × (more accurate) − (less accurate) / 63 on the values derived by the second iteration. The pattern is continued until there is one estimate.
MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
ScaLAPACK is a library of high-performance linear algebra routines for parallel distributed-memory machines that features functionality similar to LAPACK (solvers for dense and banded linear systems, least-squares problems, eigenvalue problems, and singular-value problem). Scilab is advanced numerical analysis package similar to MATLAB or Octave.
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
Let (,) = be a well-posed problem, i.e. : is a real or complex functional relationship, defined on the cross-product of an input data set and an output data set , such that exists a locally lipschitz function : called resolvent, which has the property that for every root (,) of , = ().
ALGLIB is an open source numerical analysis library with C# version. Dual licensed: GPLv2+, commercial license. ILNumerics.Net Commercial high performance, typesafe numerical array classes and functions for general math, FFT and linear algebra, aims .NET/mono, 32&64 bit, script-like syntax in C#, 2D & 3D plot controls, efficient memory management.