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Hilbert matrix — example of a matrix which is extremely ill-conditioned (and thus difficult to handle) Wilkinson matrix — example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues; Convergent matrix — square matrix whose successive powers approach the zero matrix; Algorithms for matrix multiplication:
The trend-cycle component can just be referred to as the "trend" component, even though it may contain cyclical behavior. [3] For example, a seasonal decomposition of time series by Loess (STL) [ 4 ] plot decomposes a time series into seasonal, trend and irregular components using loess and plots the components separately, whereby the cyclical ...
Another problem of extrapolation is loosely related to the problem of analytic continuation, where (typically) a power series representation of a function is expanded at one of its points of convergence to produce a power series with a larger radius of convergence. In effect, a set of data from a small region is used to extrapolate a function ...
An example of Richardson extrapolation method in two dimensions. In numerical analysis , Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A ∗ = lim h → 0 A ( h ) {\displaystyle A^{\ast }=\lim _{h\to 0}A(h)} .
This form of simple trend extrapolation helps to direct attention towards the forces, which can change the projected pattern. A more elaborated curve that uses times series analysis can often reveal surprising historical and current data patterns. The qualitative trend analysis is one of the most demanding and creative methods in Futures Studies.
In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases).
Futures studies, futures research or futurology is the systematic, interdisciplinary and holistic study of social and technological advancement, and other environmental trends, often for the purpose of exploring how people will live and work in the future.
In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. [1] It is most useful for accelerating the convergence of a sequence that is converging linearly.