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In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation.
Based on this sample, the estimated population mean is 10, and the unbiased estimate of population variance is 30. Both the naïve algorithm and two-pass algorithm compute these values correctly. Next consider the sample (10 8 + 4, 10 8 + 7, 10 8 + 13, 10 8 + 16), which gives rise to the same estimated variance as the first sample. The two-pass ...
The stability of numerical schemes can be investigated by performing von Neumann stability analysis. For time-dependent problems, stability guarantees that the numerical method produces a bounded solution whenever the solution of the exact differential equation is bounded.
CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. [3]
The NAG Library [1] can be accessed from a variety of languages and environments such as C/C++, [2] Fortran, [3] Python, [4] AD, [5] MATLAB, [6] Java [7] and .NET. [8] The main supported systems are currently Windows, Linux and macOS running on x86-64 architectures; 32-bit Windows support is being phased out. Some NAG mathematical optimization ...
The use of log probabilities improves numerical stability, when the probabilities are very small, because of the way in which computers approximate real numbers. [1] Simplicity. Many probability distributions have an exponential form. Taking the log of these distributions eliminates the exponential function, unwrapping the exponent.
[1] [2] Variants of the latter have been shown to be weakly stable (i.e. they exhibit numerical stability for well-conditioned linear systems). [3] The algorithms can also be used to find the determinant of a Toeplitz matrix in O ( n 2 ) {\displaystyle O(n^{2})} time.
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an iterative algorithm , applicable to sparse systems that are too large to be handled by a direct ...