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Newton–Raphson Method
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended to c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Methode Newton
Methode Electronics (NYSE: MEI ) is an American multinational company headquartered in Chicago, Illinois, with engineering, manufacturing and sales operations in more than 35 locations in 14 countries. The company employs around 4,566 people worldwide. References {{Authority control Companies listed on the New York Stock Exchange 1946 establishments in the United States Electrical connectors Electronics companies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halley's Method
In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it iteratively produces a sequence of approximations to the root; their rate of convergence to the root is cubic. Multidimensional versions of this method exist. Halley's method exactly finds the roots of a linear-over-linear Padé approximation to the function, in contrast to Newton's method or the Secant method which approximate the function linearly, or Muller's method which approximates the function quadratically. There is also Halley's irrational method, described below. Method Halley's method is a numerical algorithm for solving the nonlinear equation In this case, the function has to be a function of one real varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heron Of Alexandria
Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition. Hero published a well-recognized description of a steam-powered device called an ''aeolipile'', also known as "Hero's engine". Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics, he wrote a commentary on Euclid's ''Elements'' and a work on applied geometry known as the ''Metrica''. He is mostly remembered for Heron's formula; a way to calculate the area of a triangle using only the lengths of its sides. Much of Hero's original writings and designs have been lost, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Use Of Newton's Method To Compute Square Roots
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Use may refer to: * Use (law), an obligation on a person to whom property has been conveyed * Use (liturgy), subset of a Christian liturgical ritual family used by a particular group or diocese * Use–mention distinction, the distinction between using a word and mentioning it * Consumption (economics) ** Resource depletion, use to the point of lack of supply ** Psychological manipulation, in a form that treats a person is as a means to an end * Rental utilization, quantification of the use of assets to be continuously let See also * Use case, in software and systems engineering * User story, in software development and product management * USE (other) * Used (other) * User (other) Ancient Egyptian roles * User (ancient Egyptian official), an ancient Egyptian nomarch (governor) of the Eighth Dynasty * Useramen, an ancient Egyptian vizier also called "User" Other uses * User (computing), a person (or software) using an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonian Mathematics
Babylonian mathematics (also known as Assyro-Babylonian mathematics) is the mathematics developed or practiced by the people of Mesopotamia, as attested by sources mainly surviving from the Old Babylonian period (1830–1531 BC) to the Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for over a millennium. In contrast to the scarcity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from hundreds of clay tablets unearthed since the 1850s. Written in cuneiform, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics that include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approxim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and Interior (topology), interior. Intuitively speaking, a neighbourhood of a point is a Set (mathematics), set of points containing that point where one can move some amount in any direction away from that point without leaving the set. Definitions Neighbourhood of a point If X is a topological space and p is a point in X, then a neighbourhood of p is a subset V of X that includes an open set U containing p, p \in U \subseteq V \subseteq X. This is equivalent to the point p \in X belonging to the Interior (topology)#Interior point, topological interior of V in X. The neighbourhood V need not be an open subset of X. When V is open (resp. closed, compact, etc.) in X, it is called an (resp. closed neighbourhood, compact neighbourhood, etc.). Some authors require neighbourhoods to be open, so i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Of Convergence
In mathematical analysis, particularly numerical analysis, the rate of convergence and order of convergence of a sequence that converges to a limit are any of several characterizations of how quickly that sequence approaches its limit. These are broadly divided into rates and orders of convergence that describe how quickly a sequence further approaches its limit once it is already close to it, called asymptotic rates and orders of convergence, and those that describe how quickly sequences approach their limits from starting points that are not necessarily close to their limits, called non-asymptotic rates and orders of convergence. Asymptotic behavior is particularly useful for deciding when to stop a sequence of numerical computations, for instance once a target precision has been reached with an iterative root-finding algorithm, but pre-asymptotic behavior is often crucial for determining whether to begin a sequence of computations at all, since it may be impossible or imprac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, ''double roots'' counted twice). Hence the expression, "counted with multiplicity". If multiplicity is ignored, this may be emphasized by counting the number of ''distinct'' elements, as in "the number of distinct roots". However, whenever a set (as opposed to multiset) is formed, multiplicity is automatically ignored, without requiring use of the term "distinct". Multiplicity of a prime factor In prime factorization, the multiplicity of a prime factor is its p-adic valuation. For example, the prime factorization of the integer is : the multiplicity of the prime factor is , while the multiplicity of each of the prime factors and is . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differentiable Function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If is an interior point in the domain of a function , then is said to be ''differentiable at'' if the derivative f'(x_0) exists. In other words, the graph of has a non-vertical tangent line at the point . is said to be differentiable on if it is differentiable at every point of . is said to be ''continuously differentiable'' if its derivative is also a continuous function over the domain of the function f. Generally speaking, is said to be of class if its first k derivatives f^(x), f^(x), \ldots, f^(x) exist and are continuous over the domain of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton Iteration
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended to comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an "iterate") is derived from the previous ones. A specific implementation with Algorithm#Termination, termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or Quasi-Newton method, quasi-Newton methods like Broyden–Fletcher–Goldfarb–Shanno algorithm, BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called ''Convergent series, convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
