###### Newton's

- This is in contrast with other root-finding algorithms like the secant method, Sidi's generalized secant method or Newton's method, whose iterates will remain real if one starts with real numbers. (wikipedia.org)
- This can be compared with 1.62 for the secant method and 2 for Newton's method. (wikipedia.org)
- So, the secant method makes less progress per iteration than Muller's method and Newton's method makes more progress. (wikipedia.org)
- In numerical analysis, Steffensen's method is a root-finding technique similar to Newton's method, named after Johan Frederik Steffensen. (wikipedia.org)
- Steffensen's method also achieves quadratic convergence, but without using derivatives as Newton's method does. (wikipedia.org)
- a) of the initial value problem where a = y'(t0), thus a is a root of F. The usual methods for finding roots may be employed here, such as the bisection method or Newton's method. (wikipedia.org)
- In numerical analysis, Newton's method (also known as the Newton-Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. (wikipedia.org)
- However, the extra computations required for each step can slow down the overall performance relative to Newton's method, particularly if f or its derivatives are computationally expensive to evaluate. (wikipedia.org)
- The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written in 1669, published in 1711 by William Jones) and in De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson). (wikipedia.org)
- The essence of Vieta's method can be found in the work of the Persian mathematician Sharaf al-Din al-Tusi, while his successor Jamshīd al-Kāshī used a form of Newton's method to solve xP − N = 0 to find roots of N (Ypma 1995). (wikipedia.org)
- A special case of Newton's method for calculating square roots was known much earlier and is often called the Babylonian method. (wikipedia.org)
- Newton's method was used by 17th-century Japanese mathematician Seki Kōwa to solve single-variable equations, though the connection with calculus was missing. (wikipedia.org)

###### differs

- The Shettles method differs from the Ericsson method , in which the semen is deposited outside the woman and time is given for the fast/slow swimmers to separate before artificial insemination takes place. (wikipedia.org)
- Terminology used in the Vaganova method often differs from other methods, and may also vary by locale. (wikipedia.org)
- However, his method differs substantially from the modern method given above: Newton applies the method only to polynomials. (wikipedia.org)

###### algebraic

- The finite element method formulation of the problem results in a system of algebraic equations . (wikipedia.org)
- Algebraic equation sets that arise in the steady state problems are solved using numerical linear algebra methods, while ordinary differential equation sets that arise in the transient problems are solved by numerical integration using standard techniques such as Euler's method or the Runge-Kutta method. (wikipedia.org)
- Stoer and Burlisch state that there are two solutions, which can be found by algebraic methods. (wikipedia.org)
- Finally, Newton views the method as purely algebraic and makes no mention of the connection with calculus. (wikipedia.org)

###### ordinary differen

- For a boundary value problem of a second-order ordinary differential equation, the method is stated as follows. (wikipedia.org)

###### numerical method

- The finite element method ( FEM ), is a numerical method for solving problems of engineering and mathematical physics . (wikipedia.org)
- Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0. (wikipedia.org)

###### approximation

- To explain the approximation in this process, FEM is commonly introduced as a special case of Galerkin method . (wikipedia.org)
- Instead, Muller's method uses three points, constructs the parabola through these three points, and takes the intersection of the x-axis with the parabola to be the next approximation. (wikipedia.org)
- Muller's method is a recursive method which generates an approximation of the root ξ of f at each iteration. (wikipedia.org)
- Later, his Ph.D. student Louis Chen Hsiao Yun modified the method so as to obtain approximation results for the Poisson distribution, therefore the Stein method applied to the problem of Poisson approximation is often referred to as the Stein-Chen method. (wikipedia.org)
- This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated. (wikipedia.org)

###### calculus

- FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function. (wikipedia.org)
- The idea of the method is as follows: one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra). (wikipedia.org)

###### converge

- The method will usually converge, provided this initial guess is close enough to the unknown zero, and that f ′(x0) ≠ 0. (wikipedia.org)

###### mathematical

- Any project with interdependent activities can apply this method of mathematical analysis. (wikipedia.org)
- The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. (wikipedia.org)

###### citation needed

- citation needed] In the 1990s the method was adapted to a variety of distributions, such as Gaussian processes by Barbour (1990), the binomial distribution by Ehm (1991), Poisson processes by Barbour and Brown (1992), the Gamma distribution by Luk (1994), and many others. (wikipedia.org)

###### Principles

- These are principles of the scientific method, as opposed to a definitive series of steps applicable to all scientific enterprises. (wikipedia.org)
- Though the scientific method is often presented as a fixed sequence of steps, it represents rather a set of general principles. (wikipedia.org)
- In 1948, Vaganova authored a book titled "The Foundation For Dance" (more commonly known as "Basic Principles of Russian Classical Dance") that outlined her training method and ballet technique. (wikipedia.org)

###### Analyze

- In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but expensive operations. (wikipedia.org)

###### involves

- The process of the scientific method involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments or empirical observations based on those predictions. (wikipedia.org)
- A typical work out of the method involves (1) dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by (2) systematically recombining all sets of element equations into a global system of equations for the final calculation. (wikipedia.org)

###### 1971

- Method Music is an outgrowth of Townshend's groundbreaking 1971 futurist composition Lifehouse. (wikipedia.org)
- Russell G. Method (June 27, 1897 - September 17, 1971) was an American football back who played six seasons in the National Football League with the Duluth Kelleys/Eskimos and Chicago Cardinals. (wikipedia.org)

###### relatively

- Cash accounting is an accounting method that is relatively simple and is commonly used by small businesses. (investopedia.com)
- Otsu's method exhibits the relatively good performance if the histogram can be assumed to have bimodal distribution and assumed to possess a deep and sharp valley between two peaks. (wikipedia.org)

###### facilitate

- Centering Prayer is a method designed to facilitate the development of Contemplative Prayer by preparing our faculties to receive this gift. (google.com)
- To facilitate the case method of study, "law school outlines" are used as legal topic study aids. (wikipedia.org)

###### uses

- For other uses, see Scientific method (disambiguation) . (wikipedia.org)

###### dots

- The method gets its name from the overall image of the graph, which consists of many scattered dots. (investopedia.com)

###### widely

- The Delphi Method has been widely adopted and is still in use today. (rand.org)
- Today the Vaganova method is the most widely used ballet teaching method in Russia, and it is also used in Europe and North America. (wikipedia.org)

###### roots

- The method is much more difficult though for m>2 than it is for m=1 or m=2 because it is much harder to determine the roots of a polynomial of degree 3 or higher. (wikipedia.org)

###### commonly

- For example, the Vaganova "grand pas de chat" is commonly called "saut de chat" in the United States, and Vaganova's "battement jete" is often called "degage" in other methods. (wikipedia.org)

###### function

- The method approximates the unknown function over the domain. (wikipedia.org)
- The Newton-Raphson method in one variable is implemented as follows: The method starts with a function f defined over the real numbers x, the function's derivative f ′, and an initial guess x0 for a root of the function f. (wikipedia.org)
- In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. (wikipedia.org)

###### algorithm

- The critical path method ( CPM ), or critical path analysis ( CPA ), is an algorithm for scheduling a set of project activities. (wikipedia.org)
- This algorithm is first in the class of Householder's methods, succeeded by Halley's method. (wikipedia.org)

###### analysis

- As regards his method, Aristotle is recognized as the inventor of scientific method because of his refined analysis of logical implications contained in demonstrative discourse, which goes well beyond natural logic and does not owe anything to the ones who philosophized before him. (wikipedia.org)
- Alternate methods of cost estimation include the high-low method, account analysis and least squares. (investopedia.com)
- In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. (wikipedia.org)
- Direct multiple shooting method Computation of radiowave attenuation in the atmosphere Stoer, J. and Burlisch, R. Introduction to Numerical Analysis. (wikipedia.org)
- This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory. (wikipedia.org)
- clarification needed] The diagonal method was derived from an analysis of how artists intuitively locate details within a composition, and can be used for such analyses. (wikipedia.org)
- Consequently, Otsu's method is roughly a one-dimensional, discrete analog of Fisher's Discriminant Analysis. (wikipedia.org)

###### example

- The following example illustrates the use of the join method. (microsoft.com)
- A new, online method to engage more patients and caregivers in developing clinical guidelines will be created and then tested, using Duchenne muscular dystrophy as an example. (rand.org)
- The following example demonstrates this use of the All method. (microsoft.com)
- Although others before him proved theorems via the probabilistic method (for example, Szele's 1943 result that there exist tournaments containing a large number of Hamiltonian cycles), many of the most well known proofs using this method are due to Erdős. (wikipedia.org)

###### graph

- Muller's method is based on the secant method, which constructs at every iteration a line through two points on the graph of f. (wikipedia.org)

###### original

- It refers that "So far, researchers have found no morphological differences between human X sperm and Y sperm" , which seems to dismiss the original claim of Shettles Method. (wikipedia.org)
- Second Nature also released the original version of Guitar Method on 12" on October 14, 2003, in slightly abridged form. (wikipedia.org)
- The extension of the original method to multi-level thresholding is referred to as the multi Otsu method. (wikipedia.org)

###### include

- they include physicist Lee Smolin and philosopher Paul Feyerabend (in his Against Method ). (wikipedia.org)
- Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma. (wikipedia.org)

###### given

- The name of the method is given by its developer, Aviva Gabriella Steiner, a Hungarian origin Israeli ballet dancer and PE teacher. (wikipedia.org)

###### development

- The scientific method is an empirical method of knowledge acquisition which has characterized the development of science since at least the 17th century. (wikipedia.org)
- This study developed practical considerations for including large, diverse, and geographically dispersed groups of patients in clinical practice guideline development through online engagement methods. (rand.org)
- Tenets of the training method included development of lower back strength and arm plasticity, and the strength, flexibility and endurance required for ballet, and it incorporated a detailed instruction process that specified when to teach each topic and how long to teach it. (wikipedia.org)

###### value

- But, in the absence of any intuition about where the zero might lie, a "guess and check" method might narrow the possibilities to a reasonably small interval by appealing to the intermediate value theorem. (wikipedia.org)
- Another way to use the probabilistic method is by calculating the expected value of some random variable. (wikipedia.org)

###### technique

- The critical path method (CPM) is a project modeling technique developed in the late 1950s by Morgan R. Walker of DuPont and James E. Kelley Jr. of Remington Rand . (wikipedia.org)
- The Vaganova method is a ballet technique and training system devised by the Russian dancer and pedagogue Agrippina Vaganova (1879-1951). (wikipedia.org)
- The method fuses elements of traditional French style from the romantic era with the athleticism and virtuosity of Italian Cecchetti technique. (wikipedia.org)
- During the 30 years she spent teaching at the Leningrad Choreographic School, Vaganova developed a ballet technique that combined elements of French, Italian, and earlier Russian technique, and a training method to teach the technique. (wikipedia.org)

###### found

- He wanted a way to get his message clear and powerful in such a short time and found that his method was excellent for having people understand and remember his presentation. (blogs.com)

###### visual

- The method provides clear visual support for the audience and helps make the content more memorable. (blogs.com)
- Dutch photographer and lecturer Edwin Westhoff discovered the method when, after having long taught the rule of thirds in photography courses, he conducted visual experiments to investigate why this rule of thirds only loosely prescribes that points of interest should be placed more or less near the intersection of lines, rather than being rigid and demanding placement to be precisely on these intersections. (wikipedia.org)

###### similar

- The Householder's methods are similar but have higher order for even faster convergence. (wikipedia.org)
- Newton may have derived his method from a similar but less precise method by Vieta. (wikipedia.org)
- The casebook method, similar to but not exactly the same as the case method, is the primary method of teaching law in law schools in the United States. (wikipedia.org)

###### results

- Later on, one of Aviva Gabriella Steiner's students, a Hungarian yoga instructor and PE teacher, Livia Toth combined the method with diet and reached good results with several feminine health problems. (wikipedia.org)
- Then the possibly incorrect threshold determined by Otsu's method results in the segmentation error. (wikipedia.org)

###### process

- Though there are diverse models for the scientific method available, in general there is a continuous process that includes observations about the natural world. (wikipedia.org)
- The method entails a group of experts who anonymously reply to questionnaires and subsequently receive feedback in the form of a statistical representation of the "group response," after which the process repeats itself. (rand.org)

###### however

- There are difficulties in a formulaic statement of method, however. (wikipedia.org)
- If a business generates more than $5 million in annual sales, however, it must use the accrual method, according to Internal Revenue Service rules. (investopedia.com)

###### general

- Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. (wikipedia.org)

###### known

- This is known as the percentage of completion method. (investopedia.com)
- One famous and effective way is known as two-dimensional Otsu's method. (wikipedia.org)

###### points

- Muller's method fits a parabola, i.e. a second-order polynomial, to the last three obtained points f(xk-1), f(xk-2) and f(xk-3) in each iteration. (wikipedia.org)

###### elements

- This method does not return all the elements of a collection. (microsoft.com)

###### follows

- Accounting method refers to the rules a company follows in reporting revenues and expenses. (investopedia.com)

###### idea

- Takahashi says that the method is really designed for people who are not good at presentations and who are quite nervous about the idea of presenting. (blogs.com)
- Robert Nola and Howard Sankey remark that "For some, the whole idea of a theory of scientific method is yester-year's debate, the continuation of which can be summed up as yet more of the proverbial deceased equine castigation. (wikipedia.org)
- The Shettles Method is a child conception idea that is reputed to help determine a baby's sex. (wikipedia.org)
- The idea of a musical portraiture system was first explored by Townshend in the lead-off cut on Who's Next, Baba O'Riley - a piece echoed in Meher Baba Piece, the first track on Method Music (which was included on The Who's 2006 album Endless Wire as the underpinning for Fragments, co-written by Ball). (wikipedia.org)

###### primary

- Two primary methods are accrual accounting and cash accounting. (investopedia.com)

###### official

- TV anime Celestial Method official website] (in Japanese). (wikipedia.org)

###### study

- To set up the case method of law study, American law professors traditionally collect the most illustrative cases concerning a particular area of the law in special textbooks called casebooks. (wikipedia.org)

###### performance

- Accrual accounting is an important method of measuring the performance and position of a company. (investopedia.com)

###### website

- In 2007, Townshend launched The Lifehouse Method website, run by his company Eel Pie, an online music portraiture system created with Ball and programmer Dave Snowdon in which users entered data into the system and received a unique, customized piece of audio. (wikipedia.org)

###### system

- Method (Ancient Greek: μέθοδος, methodos) literally means a pursuit of knowledge, investigation, mode of prosecuting such inquiry, system. (wikipedia.org)
- Method Music is a double-album of electronic music by the English composer and mathematician Lawrence Ball created using the compositional system that would become The Lifehouse Method, an online-based compositional project conceived by Pete Townshend of The Who to compose customized algorithmically-generated musical portraits. (wikipedia.org)
- Aviva Method or Aviva Dance is a physical exercise system that claims to stimulate the related glands for optimal reproductive hormone secretion. (wikipedia.org)

###### years

- Predating Guitar Method by three years, Second Nature Recordings released a 7-inch Kid Kilowatt single entitled Hit Single in 2001. (wikipedia.org)

###### works

- Medical experts do not agree that the method works. (wikipedia.org)
- The large majority of the literature recommended by the Carden Method is classical, including works such as The Aeneid, The Adventures of Huckleberry Finn, and The Last of the Mohicans. (wikipedia.org)

###### simple

- While the method is simple, it is also imprecise. (investopedia.com)

###### business

- While it may not be a perfect method or applicable in all situations, it is still far better than the method used by most business people in Japan. (blogs.com)
- Business managers use the scattergraph method in cost estimation to anticipate operating costs at different activity levels. (investopedia.com)

###### order

- The Delphi method solicits the opinions of experts through a series of carefully designed questionnaires interspersed with information and opinion feedback in order to establish a convergence of opinion. (rand.org)
- The order of convergence of Muller's method is approximately 1.84. (wikipedia.org)

###### people

- One such person is Mr. Masayoshi Takahashi who has gotten a lot of people interested in his unique way of presenting, now labeled the 'Takahashi Method. (blogs.com)
- Over the past year, blogs across Japan have been buzzing about Takahashi and his presentation style and people began calling it the 'Takahashi Method. (blogs.com)

###### track

- This method, then, is easy to do, helps the presenter get organized during planning and keeps the presenter on track while presenting. (blogs.com)

###### obtain

- Taking m=1 we obtain the secant method whereas m=2 gives Muller's method. (wikipedia.org)

###### possible

- Probably the most important contributions are the monograph by Stein (1986), where he presents his view of the method and the concept of auxiliary randomisation, in particular using exchangeable pairs, and the articles by Barbour (1988) and Götze (1991), who introduced the so-called generator interpretation, which made it possible to easily adapt the method to many other probability distributions. (wikipedia.org)

###### approximately

- The Carden Method is an educational program developed by Mae Carden and practiced in approximately 80 K-8 schools across the United States. (wikipedia.org)