Search results
Results from the WOW.Com Content Network
In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series.It depends on the quantity | |, where are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one.
The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not ...
Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis depends on which version of the test is used, but is usually stationarity or trend-stationarity .
Newton's method is a powerful technique—if the derivative of the function at the root is nonzero, then the convergence is at least quadratic: as the method converges on the root, the difference between the root and the approximation is squared (the number of accurate digits roughly doubles) at each step. However, there are some difficulties ...
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965. [1]Newton's method for solving f(x) = 0 uses the Jacobian matrix, J, at every iteration.
Which of the three main versions of the test should be used is not a minor issue. The decision is important for the size of the unit root test (the probability of rejecting the null hypothesis of a unit root when there is one) and the power of the unit root test (the probability of rejecting the null hypothesis of a unit root when there is not one).