List of mathematics-based methods
Encyclopedia
This is a list of mathematics-based methods, by Wikipedia page.
See also list of graphical methods.
See also list of graphical methods.
- Adams' method (differential equations)
- Akra-Bazzi methodAkra-Bazzi methodIn computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes...
(asymptotic analysisAsymptotic analysisIn mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are...
) - Condorcet method Condorcet methodA Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
(voting systems) - Coombs' methodCoombs' methodThe Coombs' method is a voting system created by Clyde Coombs used for single-winner elections in which each voter rank the candidates in order of preference. It is very similar to instant-runoff voting , a more common preferential voting system.-Procedures:Each voter rank-orders all of the...
(voting systems) - Copeland's method Copeland's methodCopeland's method or Copeland's pairwise aggregation method is a Condorcet method in which candidates are ordered by the number of pairwise victories, minus the number of pairwise defeats....
(voting systems) - Crank–Nicolson method (numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - D'Hondt methodD'Hondt methodThe d'Hondt method is a highest averages method for allocating seats in party-list proportional representation. The method described is named after Belgian mathematician Victor D'Hondt who described it in 1878...
(voting systems) - Discrete element methodDiscrete element methodA discrete element method , also called a distinct element method is any of family of numerical methods for computing the motion of a large number of particles of micrometre-scale size and above...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Domain decomposition methodDomain decomposition methodIn mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.- Overview :...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Epidemiological methodsEpidemiological methodsThe science of epidemiology has matured significantly from the times of Hippocrates and John Snow. The techniques for gathering and analyzing epidemiological data vary depending on the type of disease being monitored but each study will have overarching similarities....
- Euler's backward method
- Euler's forward method
- Explicit and implicit methodsExplicit and implicit methodsExplicit and implicit methods are approaches used in numerical analysis for obtaining numerical solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes....
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Finite difference methodFinite difference methodIn mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.- Derivation from Taylor's polynomial :...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Finite element methodFinite element methodThe finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Finite volume methodFinite volume methodThe finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations [LeVeque, 2002; Toro, 1999]....
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Highest averages methodHighest averages methodThe highest averages method is the name for a variety of ways to allocate seats proportionally for representative assemblies with party list voting systems....
(voting systems) - Method of exhaustionMethod of exhaustionThe method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will...
- Method of infinite descent (number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
) - Information bottleneck methodInformation bottleneck methodThe information bottleneck method is a technique introduced by Naftali Tishby et al. [1] for finding the best tradeoff between accuracy and complexity when summarizing a random variable X, given a joint probability distribution between X and an observed relevant variable Y...
- Inverse chain rule method (calculusCalculusCalculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
) - Inverse transform sampling methodInverse transform sampling methodInverse transform sampling, also known as the inverse probability integral transform or inverse transformation method or Smirnov transform or even golden rule, is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given...
(probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
) - Iterative method Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Jacobi methodJacobi methodIn numerical linear algebra, the Jacobi method is an algorithm for determining the solutions of a system of linear equations with largest absolute values in each row and column dominated by the diagonal element. Each diagonal element is solved for, and an approximate value plugged in. The process...
(linear algebraLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
) - Largest remainder methodLargest remainder methodThe largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems...
(voting systems) - Level set methodLevel set methodThe level set method is a numerical technique for tracking interfaces and shapes. The advantage of the level set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects...
- Linear combination of atomic orbitals molecular orbital methodLinear combination of atomic orbitals molecular orbital methodA linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions...
(molecular orbitals) - Method of characteristicsMethod of characteristicsIn mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation...
- Least squares method (optimizationOptimization (mathematics)In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
, statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
) - Maximum likelihood method (statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
) - Method of complementsMethod of complementsIn mathematics and computing, the method of complements is a technique used to subtract one number from another using only addition of positive numbers. This method was commonly used in mechanical calculators and is still used in modern computers...
(arithmeticArithmeticArithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
) - Method of moving frames (differential geometry)
- Method of successive substitutionMethod of successive substitutionIn modular arithmetic, the method of successive substitution is a method of solving problems of simultaneous congruences by using the definition of the congruence equation...
(number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
) - Monte Carlo methodMonte Carlo methodMonte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
(computational physicsComputational physicsComputational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists...
, simulationSimulationSimulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
) - Newton's methodNewton's methodIn numerical analysis, Newton's method , named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots of a real-valued function. The algorithm is first in the class of Householder's methods, succeeded by Halley's method...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Perturbation methods (functional analysisFunctional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, quantum theoryQuantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
) - Probabilistic methodProbabilistic methodThe 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. It works by showing that if one randomly chooses objects from a specified class, the probability that the...
(combinatoricsCombinatoricsCombinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
) - Romberg's methodRomberg's methodIn numerical analysis, Romberg's method is used to estimate the definite integral \int_a^b f \, dx by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule . The estimates generate a triangular array...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Runge-Kutta method (numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Sainte-Laguë methodSainte-Laguë methodThe Sainte-Laguë method is one way of allocating seats approximately proportional to the number of votes of a party to a party list used in many voting systems. It is named after the French mathematician André Sainte-Laguë. The Sainte-Laguë method is quite similar to the D'Hondt method, but uses...
(voting systems) - Schulze methodSchulze methodThe Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners...
(voting systems) - Sequential Monte Carlo method
- Simplex method
- Spectral methodSpectral methodSpectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain Dynamical Systems, often involving the use of the Fast Fourier Transform. Where applicable, spectral methods have excellent error properties, with the so called "exponential...
(numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
) - Variational methods (mathematical analysisMathematical analysisMathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, differential equationDifferential equationA differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s) - Welch methodWelch methodIn physics, engineering, and applied mathematics, Welch's method, named after P.D. Welch, is used for estimating the power of a signal at different frequencies: that is, is is an approach to spectral density estimation. The method is based on the concept of using periodogram spectrum estimates,...