82 relations: Aitken's delta-squared process, Almost all, Arthur Cayley, Attractor, Banach space, Bessel function, Bisection method, Calculus, Chaos theory, Complex analysis, Complex-valued function, De analysi per aequationes numero terminorum infinitas, Derivative, Division by zero, Elementary algebra, Endre Süli, Euler method, Fast inverse square root, Fractal, François Viète, Fréchet derivative, Function (mathematics), Functional (mathematics), Gauss–Newton algorithm, Generalized inverse, Gradient descent, Graph of a function, Halley's method, Hensel's lemma, Hessian matrix, Householder's method, Integer square root, Intermediate value theorem, Interval (mathematics), Isaac Newton, Iterative method, Jacobian matrix and determinant, Jamshīd al-Kāshī, John Colson, John Wallis, Joseph Fourier, Joseph Raphson, Kantorovich theorem, Laguerre's method, Leonid Kantorovich, Limit of a sequence, Mathematics in medieval Islam, Method of Fluxions, Methods of computing square roots, Multiplicative inverse, ..., Multiplicity (mathematics), Neighbourhood (mathematics), Newton fractal, Newton's method in optimization, Non-linear least squares, Numerical analysis, Peter Henrici (mathematician), Power series, Q-analog, Quasi-Newton method, Rate of convergence, Real number, Richardson extrapolation, Root-finding algorithm, Secant method, Second derivative, Seki Takakazu, Sequence, Sharaf al-Dīn al-Ṭūsī, Stationary point, Steffensen's method, Subgradient method, System of linear equations, Tangent, Taylor's theorem, The College Mathematics Journal, The Mathematical Gazette, Thomas Simpson, Transcendental equation, Transcendental function, William Jones (mathematician), Zero of a function. Expand index (32 more) » « Shrink index
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.
In mathematics, the term "almost all" means "all but a negligible amount".
Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.
In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
The bisection method in mathematics is a root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing.
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
In mathematics, a complex-valued function (not to be confused with complex variable function) is a function whose values are complex numbers.
De analysi per aequationes numero terminorum infinitas (or On analysis by infinite series, On Analysis by Equations with an infinite number of terms, On the Analysis by means of equations of an infinite number of terms,About completely loosening infinity by way of number equalisations limits) cf. (aequatio, analysi.
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
In mathematics, division by zero is division where the divisor (denominator) is zero.
Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.
Endre Süli (also, Endre Suli) is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford and Supernumerary Fellow of Linacre College, Oxford.
In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format.
In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.
François Viète (Franciscus Vieta; 1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations.
In mathematics, the Fréchet derivative is a derivative defined on Banach spaces.
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
In mathematics, the term functional (as a noun) has at least two meanings.
The Gauss–Newton algorithm is used to solve non-linear least squares problems.
In mathematics, and in particular, algebra, a generalized inverse of an element x is an element y that has some properties of an inverse element but not necessarily all of them.
Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
In numerical analysis, Halley’s method is a root-finding algorithm used for functions of one real variable with a continuous second derivative.
In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number, then this root corresponds to a unique root of the same equation modulo any higher power of, which can be found by iteratively "lifting" the solution modulo successive powers of.
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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.
In number theory, the integer square root (isqrt) of a positive integer n is the positive integer m which is the greatest integer less than or equal to the square root of n, For example, \mbox(27).
In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval,, as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) (غیاث الدین جمشید کاشانی Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.
John Colson (1680–1760) was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.
John Wallis (3 December 1616 – 8 November 1703) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus.
Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations.
Joseph Raphson (c. 1648 – c. 1715) was an English mathematician known best for the Newton–Raphson method.
The Kantorovich theorem (Newton-Kantorovich theorem) is a mathematical statement on the convergence of Newton's method.
In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials.
Leonid Vitaliyevich Kantorovich (a) (19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources.
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).
Method of Fluxions is a book by Isaac Newton.
In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(Z)\in\mathbb or transcendental function.
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to), also known as the stationary points of.
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n).
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
Peter Karl Henrici (13 September 1923 – 13 March 1987) was a Swiss mathematician best known for his contributions to the field of numerical analysis.
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as.
Quasi-Newton methods are methods used to either find zeroes or local maxima and minima of functions, as an alternative to Newton's method.
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence.
In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method.
In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of.
, also known as,Selin, was a Japanese mathematician and author of the Edo period.
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
(c. 1135 – c. 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages).
In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.
In numerical analysis, Steffensen's method is a root-finding technique similar to Newton's method, named after Johan Frederik Steffensen.
Subgradient methods are iterative methods for solving convex minimization problems.
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.
The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years.
The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.
Thomas Simpson FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the eponymous Simpson's rule to approximate definite integrals.
A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for.
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his use of the symbol (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter.
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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