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59 relations: Advection, Algorithm, Approximation theory, Banach space, Barycentric coordinate system, Bicubic interpolation, Bilinear interpolation, Brahmagupta's interpolation formula, Chebyshev polynomials, Computational complexity theory, Curve fitting, Degree of a polynomial, Dependent and independent variables, Derivative, Division by zero, Engineering, Experiment, Extrapolation, Fourier series, Function approximation, Gaussian process, Hermite interpolation, Imputation (statistics), Interpolation, Isolated point, JavaScript, Kriging, Lagrange polynomial, Least squares, Linear function, Linearity, Marcinkiewicz interpolation theorem, Mathematics, Missing data, Multivariate interpolation, Newton–Cotes formulas, Numerical analysis, Padé approximant, Piecewise, Polynomial, Polynomial interpolation, Rational function, Riesz–Thorin theorem, Runge's phenomenon, Sampling (statistics), Science, Simple rational approximation, Smoothness, Spline (mathematics), Spline interpolation, ..., Topological space, Transportation theory (mathematics), Trigonometric interpolation, Trigonometric polynomial, Trilinear interpolation, Unit of observation, Upsampling, Wavelet, Whittaker–Shannon interpolation formula. Expand index (9 more) »
Advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance by bulk motion.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Barycentric coordinate system
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.
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Bicubic interpolation
In mathematics, bicubic interpolation is an extension of cubic interpolation for interpolating data points on a two-dimensional regular grid.
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Bilinear interpolation
In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables (e.g., x and y) on a rectilinear 2D grid.
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Brahmagupta's interpolation formula
Brahmagupata's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta (598–668 CE) in the early 7th century CE.
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Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
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Degree of a polynomial
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Derivative
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).
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Division by zero
In mathematics, division by zero is division where the divisor (denominator) is zero.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Experiment
An experiment is a procedure carried out to support, refute, or validate a hypothesis.
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Extrapolation
In mathematics, extrapolation is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Function approximation
In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way.
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Gaussian process
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed.
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Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of interpolating data points as a polynomial function.
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Imputation (statistics)
In statistics, imputation is the process of replacing missing data with substituted values.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Isolated point
In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S but there exists a neighborhood of x which does not contain any other points of S. This is equivalent to saying that the singleton is an open set in the topological space S (considered as a subspace of X).
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JavaScript
JavaScript, often abbreviated as JS, is a high-level, interpreted programming language.
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Kriging
In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances, as opposed to a piecewise-polynomial spline chosen to optimize smoothness of the fitted values.
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Lagrange polynomial
In numerical analysis, Lagrange polynomials are used for polynomial interpolation.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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Linear function
In mathematics, the term linear function refers to two distinct but related notions.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Marcinkiewicz interpolation theorem
In mathematics, the Marcinkiewicz interpolation theorem, discovered by, is a result bounding the norms of non-linear operators acting on ''L''p spaces.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Missing data
In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation.
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Multivariate interpolation
In numerical analysis, multivariate interpolation or spatial interpolation is interpolation on functions of more than one variable.
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Newton–Cotes formulas
In numerical analysis, the Newton–Cotes formulae, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally spaced points.
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Numerical analysis
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).
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Padé approximant
In mathematics a Padé approximant is the 'best' approximation of a function by a rational function of given order – under this technique, the approximant's power series agrees with the power series of the function it is approximating.
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Piecewise
In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain, a sub-domain.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Polynomial interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.
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Rational function
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
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Riesz–Thorin theorem
In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem is a result about interpolation of operators.
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Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.
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Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population.
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Science
R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.
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Simple rational approximation
Simple rational approximation (SRA) is a subset of interpolating methods using rational functions.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Spline (mathematics)
In mathematics, a spline is a function defined piecewise by polynomials.
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Spline interpolation
In the mathematical field of numerical analysis, Spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Transportation theory (mathematics)
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources.
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Trigonometric interpolation
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials.
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Trigonometric polynomial
In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n taking on the values of one or more natural numbers.
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Trilinear interpolation
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid.
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Unit of observation
In statistics, a unit of observation is the unit described by the data that one analyzes.
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Upsampling
In digital signal processing, upsampling can refer to the entire process of increasing the sampling rate of a signal, or it can refer to just one step of the process, the other step being interpolation.
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Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero.
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Whittaker–Shannon interpolation formula
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers.
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References
[1] https://en.wikipedia.org/wiki/Interpolation
