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Householder's Method
In mathematics, and more specifically in numerical analysis, Householder's methods are a class of root-finding algorithms that are used for functions of one real variable with continuous derivatives up to some order . Each of these methods is characterized by the number , which is known as the ''order'' of the method. The algorithm is iterative and has a rate of convergence of . These methods are named after the American mathematician Alston Scott Householder. Method Householder's method is a numerical algorithm for solving the nonlinear equation . In this case, the function has to be a function of one real variable. The method consists of a sequence of iterations :x_ = x_n + d\; \frac beginning with an initial guess . If is a times continuously differentiable function and is a zero of but not of its derivative, then, in a neighborhood of , the iterates satisfy: :, x_ - a , \le K \cdot ^ , for some K > 0.\! This means that the iterates converge to the zero if th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
