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Interpolation on functions of more than one variable
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable
Multivariate_interpolation
Method for estimating new data within known data points
unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable
Interpolation
Method of interpolating functions on a 2D grid
mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually
Bilinear_interpolation
Method of multivariate interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one
Nearest-neighbor interpolation
Nearest-neighbor_interpolation
Surface-approximation method
In the mathematical subfield numerical analysis, tricubic interpolation is a method for obtaining values at arbitrary points in 3D space of a function
Tricubic_interpolation
Topics referred to by the same term
calculus Multivariate function Multivariate polynomial Multivariate interpolation Multivariate optimization Multivariate cryptography Multivariate division
Multivariate
Extension of cubic spline interpolation
In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating
Bicubic_interpolation
Method of multivariate interpolation on a 3-dimensional regular grid
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate
Trilinear_interpolation
Technique in signal processing
fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has been
Lanczos_resampling
Type of deterministic method for multivariate interpolation
distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known homogeneously scattered set of points. The assigned
Inverse_distance_weighting
Method of spatial interpolation
neighbor interpolation has also been developed that gives a measure of interpolation uncertainty. Inverse distance weighting Multivariate interpolation Sibson
Natural-neighbor interpolation
Natural-neighbor_interpolation
Mathematical method
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial
Spline_interpolation
Method of representing curves and surfaces in computer graphics
everywhere else. Effectively, N i , n {\displaystyle N_{i,n}} is a linear interpolation of N i , n − 1 {\displaystyle N_{i,n-1}} and N i + 1 , n − 1 {\displaystyle
Non-uniform_rational_B-spline
Cubic function used for interpolation
dimensions Tricubic interpolation, a generalization to three dimensions Hermite interpolation Multivariate interpolation Spline interpolation Discrete spline
Cubic_Hermite_spline
Color reconstruction algorithm
fringes and some roughness). These algorithms are examples of multivariate interpolation on a uniform grid, using relatively straightforward mathematical
Demosaicing
c0(0) = d0(0), c0(1) = d1(0), c1(0) = d0(1), c1(1) = d1(1); linear interpolation can be used to interpolate between c0 and c1, that is L c ( s , t )
Coons_patch
Method of curve fitting
In mathematics, linear interpolation (sometimes lerp) is a method of curve fitting using linear polynomials to construct new data points within the range
Linear_interpolation
Method of function approximation and data interpolation
polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in
Polyharmonic_spline
Technique in 3D computer graphics
application of subdivision surfaces. DeRose wrote about "efficient, fair interpolation" and character animation. Stam described a technique for a direct evaluation
Catmull–Clark subdivision surface
Catmull–Clark_subdivision_surface
Species of mathematical spline
a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in
Bézier_surface
Form of interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through
Polynomial_interpolation
Method of interpolation
linear statistics Gaussian process Multivariate interpolation Nonparametric regression Radial basis function interpolation Space mapping Spatial dependence
Kriging
Image interpolation method
to computer graphics, nearest neighbor value interpolation is an advanced method of image interpolation. This method fills the empty location with pixel
Nearest neighbor value interpolation
Nearest_neighbor_value_interpolation
Curved curface derived from a coarse polygon mesh
Computer graphics and interactive techniques, doi Nasri, A. H. Surface interpolation on irregular networks with normal conditions. Computer Aided Geometric
Subdivision_surface
Generalization of basis splines (B-splines) to multiple variables
considered as a multivariate generalization of basis splines (B-splines) and are generally used for multivariate approximation/interpolation. Geometrically
Box_spline
Type of polygon mesh in computer graphics
In 3D computer graphics, a Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines,
Doo–Sabin_subdivision_surface
Bézier surface created by control point interpolation
surface that is created by (linear, quadratic, cubic or higher degree) interpolation of control points. A general nth-order Bézier triangle has (n +1)(n + 2)/2
Bézier_triangle
Topics referred to by the same term
processing) Signal (information theory) Data conversion Interpolation Multivariate interpolation Subsampling (disambiguation) This disambiguation page lists
Resampling
interpolated. Multivariate interpolation Bicubic interpolation: a generalization of cubic interpolation to two dimensions Bilinear interpolation: an extension
List_of_algorithms
Type of polynomial
variables. This is a specific form of multivariate interpolation, not to be confused with piecewise linear interpolation. The resulting polynomial is not a
Multilinear_polynomial
Mathematical function with multiple real-number arguments
In mathematics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being
Function of several real variables
Function_of_several_real_variables
Mathematical technique used in environmental sciences
Trend surface analysis, also known as trend surface mapping, is a mathematical technique used in archaeology and environmental sciences such as geology
Trend_surface_analysis
Method of data interpolation and smoothing
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are
Thin_plate_spline
Type of mathematical function
basis functions were first introduced by Powell to solve the real multivariate interpolation problem. Broomhead & Lowe 1988, p. 347: "We would like to thank
Radial_basis_function
Sequence of data points over time
analysis may also be divided into linear and non-linear, and univariate and multivariate. A time series is one type of panel data. Panel data is the general class
Time_series
Changing the sampling rate of a discrete signal
[self-published source?] Sample rate conversion in multiple dimensions: Multivariate interpolation Techniques and processing that may involve sample-rate conversion:
Sample-rate_conversion
Bloor-Wilson PDE Surface Model by using Canonical Basis for Hermite Interpolation, Mathematical Engineering in Industry, 7(4), 421-33 (1999). H. Du and
PDE_surface
Branch of statistics focusing on spatial data sets
geography Concepts and Techniques in Modern Geography Multivariate interpolation Spline interpolation Geodemographic segmentation Geodesy Geographic Information
Geostatistics
Subdivision surface derived from a triangular mesh
In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular
Loop_subdivision_surface
Association of one output to each input
whether 0 belongs to its domain of definition (see Halting problem). A multivariate function, multivariable function, or function of several variables is
Function_(mathematics)
Statistical model
Gaussian processes are thus useful as a powerful non-linear multivariate interpolation tool. Kriging is also used to extend Gaussian process in the case
Gaussian_process
positive semi-definite Multivariate interpolation — the function being interpolated depends on more than one variable Barnes interpolation — method for two-dimensional
List of numerical analysis topics
List_of_numerical_analysis_topics
Image processing methods
and multivariate interpolation: Nearest-neighbor interpolation linear interpolation bilinear interpolation cubic interpolation bicubic interpolation Bézier
Video_post-processing
Algebraic structure
univariate case, one can also consider formal partial derivatives in the multivariate case for polynomials. Given a ground field K {\displaystyle K} and the
Polynomial_ring
Non-parametric regression technique
In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric
Multivariate adaptive regression spline
Multivariate_adaptive_regression_spline
Middle quantile of a data set or probability distribution
Niinimaa, A., and H. Oja. "Multivariate median." Encyclopedia of statistical sciences (1999). Mosler, Karl. Multivariate Dispersion, Central Regions
Median
Type of mathematical expression
polynomials are widely used, for example in trigonometric interpolation applied to the interpolation of periodic functions. They are also used in the discrete
Polynomial
Mathematical function defined piecewise by polynomials
polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when
Spline_(mathematics)
Concept in machine learning
in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number
Double_descent
Algorithms for zeros of functions
in the neighborhood of the root. Many root-finding processes work by interpolation. This consists in using the last computed approximate values of the
Root-finding_algorithm
British mathematician (1944–2017)
"A brief description of natural neighbour interpolation", in Barnett, Vic (ed.), Interpreting multivariate data, Chichester West Sussex New York: Wiley
Robin_Sibson
Chart displaying multivariate data
a common method of visualizing high-dimensional datasets to analyze multivariate data having multiple variables, or attributes. To plot, or visualize
Parallel_coordinates
Algorithm for multiplying large numbers
has five main steps: Splitting Evaluation Pointwise multiplication Interpolation Recomposition In a typical large integer implementation, each integer
Toom–Cook_multiplication
Discrete analog of a derivative
equation, named after Isaac Newton; in essence, it is the Gregory–Newton interpolation formula (named after Isaac Newton and James Gregory), first published
Finite_difference
Data visualisation technique
originally developed by Daniel Asimov 1980–85, which is used to explore multivariate statistical data by means of an animation. The animation, or "movie"
Grand Tour (data visualisation)
Grand_Tour_(data_visualisation)
Brazilian biostatistician
University in Canada. She is known for her research on spatiotemporal and multivariate statistics and their applications in environmental statistics and epidemiology
Alexandra_M._Schmidt
Statistic which divides a data set into 100 parts and analyzes it as a percentage
methods that return a score from the distribution, although compared to interpolation methods, results can be a bit crude. The Nearest-Rank Methods table
Percentile
Types of numerical variables in mathematics
control group). A mixed multivariate model can contain both discrete and continuous variables. For instance, a simple mixed multivariate model could have a
Continuous or discrete variable
Continuous_or_discrete_variable
Problem of determining whether polynomials are identical
Singer, Michael F., "Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields", SIAM J. Comput., Vol 19, No.6, pp.
Polynomial_identity_testing
Mathematical framework
functional connections (TFC) is a mathematical framework for functional interpolation. It provides a method for deriving a functional—a function that operates
Theory of functional connections
Theory_of_functional_connections
Set of statistical processes for estimating the relationships among variables
algorithm) Local regression Modifiable areal unit problem Multivariate adaptive regression spline Multivariate normal distribution Pearson correlation coefficient
Regression_analysis
Tool in multivariate statistical analysis
geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis on metric spaces. It is named after the Swedish
Matérn_covariance_function
Root-finding algorithm
approximations to the root; their rate of convergence to the root is cubic. Multivariate versions of this method exist. Halley's method exactly finds the roots
Halley's_method
Italian mathematician and professor
′′Four lectures on radial basis functions″ and '′Lectures on multivariate polynomial interpolation″. Bos., Len; Sommariva, Alvise; Perracchione, Emma; Santin
Stefano_De_Marchi
Scientific method for biochronology
biochronology through the ordering of the appearance of fossil mammal genera by multivariate analysis, using conjunctional (overlapping) and disconjunctional (nonoverlapping)
Appearance_event_ordination
Function whose all derivatives vanish at a point
{\displaystyle C_{2}} inhabit R n {\displaystyle \mathbb {R} ^{n}} . A smooth interpolation between C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} , between
Flat_function
more reliable than those outside, as the model is primarily valid for interpolation within the training data space, rather than extrapolation. For example
Applicability_domain
Measure of statistical dispersion
divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1 (also called the lower quartile)
Interquartile_range
2002-11-06. Keith J. Worsley, An unbiased estimator for the roughness of a multivariate Gaussian random field, Technical report, 2000 July. Keith J. Worsley
Resel
Type of signal in signal processing
Gaussian white noise vector. In that case, the joint distribution of w is a multivariate normal distribution; the independence between the variables then implies
White_noise
Spatial prediction technique
and thematic maps) with interpolation (kriging) of the regression residuals. It is mathematically equivalent to the interpolation method variously called
Regression-kriging
Matrix of geometric progressions
are equal), making the Vandermonde matrix invertible. The polynomial interpolation problem is to find a polynomial p ( x ) = a 0 + a 1 x + a 2 x 2 + ⋯
Vandermonde_matrix
Danish astronomer
actuary and mathematician, most notable for his work in statistics, interpolation and the three-body problem. Thiele made notable contributions to the
Thorvald_N._Thiele
Spline function
filtering with a rectangle function, higher-order interpolation is obtained. Fast B-spline interpolation on a uniform sample domain can be done by iterative
B-spline
facilities for: Probability distributions: discrete, continuous and multivariate. Pseudo-random number generation, including Mersenne Twister MT19937
Math.NET_Numerics
Special mathematical function defined as sin(x)/x
Basel problem. The product of 1-D sinc functions readily provides a multivariate sinc function for the square Cartesian grid (lattice): sincC(x, y) =
Sinc_function
developmental and evolutionary theories. This led to the first branch of multivariate morphometrics, which emphasized matrix manipulations involving variables
Geometric morphometrics in anthropology
Geometric_morphometrics_in_anthropology
Mathematical function
_{n})}{\Gamma (\alpha _{1}+\alpha _{2}+\cdots +\alpha _{n})}}.} This multivariate beta function is used in the definition of the Dirichlet distribution
Beta_function
Multivariate kernel density estimation Multivariate normal distribution Multivariate Pareto distribution Multivariate Pólya distribution Multivariate
List_of_statistics_articles
permanent of a matrix, it is clear that PERM(M) for any n-by-n matrix M is a multivariate polynomial of degree n over the entries in M. Calculating the permanent
Random_self-reducibility
Type of error-correcting codes
shows us that the interpolation step can be done in near-linear time. For now, we have talked about everything we need for the multivariate polynomial Q (
Folded_Reed–Solomon_code
Statistics concept
polynomial regression Polynomial and rational function modeling Polynomial interpolation Response surface methodology Smoothing spline Microsoft Excel makes
Polynomial_regression
American mathematician
to the theory of total positivity, multivariate splines, refinability, geometric modeling, wavelets, interpolation by radial functions, neural networks
Charles_Anthony_Micchelli
Probability distribution
probability. The univariate Pareto distribution has been extended to a multivariate Pareto distribution. The likelihood function for the Pareto distribution
Pareto_distribution
Non-parametric classification method
value of that single nearest neighbor, also known as nearest neighbor interpolation. For both classification and regression, a useful technique can be to
K-nearest_neighbors_algorithm
Examples of curve-fitting compaction consisting of discretization and then interpolation are: Breaking of a continuous curve into a series of straight line segments
Curve-fitting_compaction
Option pricing model
application to the multivariate case, where a multivariate model has been formulated that is consistent with a mixture of multivariate lognormal densities
Local_volatility
Statistical concept
not usually imputed. In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete
Missing_data
Waleed. Temporal classification: Extending the classification paradigm to multivariate time series. Diss. The University of New South Wales, 2002. Graves, Alex
List of datasets for machine-learning research
List_of_datasets_for_machine-learning_research
Specifies a range of position-dependent colors
color-blind people ( colorblind-friendly) color space color depth 1D 2D: Multivariate map, bivariate or trivariate 3D An axial color gradient (sometimes also
Color_gradient
Spatial interpolation and Kriging Felus, Y. A.; Saalfeld, A.; Schaffrin, B. (2005). "Delaunay Triangulation Structured Kriging for Surface Interpolation". Surveying
Yaron_Felus
Polynomial sequence
ISSN 0196-8858. Ismail, Mourad E. H.; Zhang, Ruiming (2017-04-01). "A review of multivariate orthogonal polynomials". Journal of the Egyptian Mathematical Society
Hermite_polynomials
Describes approximate behavior of a function
where the domain is finite, infinite, real, complex, single variate, or multivariate. In most applications, one chooses the function g ( x ) {\displaystyle
Big_O_notation
Cryptanalytic attacks using a system of multivariate equations
then each Boolean function f {\displaystyle f} can be represented as a multivariate polynomial over GF(2) which is called the algebraic normal form (ANF)
Algebraic_attack
50 (1983), 277–319. A. Lindquist and G. Picci, Realization theory for multivariate stationary Gaussian processes, SIAM J. Control and Optimization 23 (1985)
Anders_Lindquist
solution methods can be used. The TFC theory has been developed for multivariate rectangular domains subject to absolute, integral, relative, and linear
Daniele_Mortari
Algorithm for measuring similarity between temporal sequences
sequence into uniform segments that are scaled in time using linear interpolation, to produce the best matching warping. The segment scaling causes potential
Dynamic_time_warping
Computational method
Kronecker rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension. But most of the
Factorization_of_polynomials
Algorithm that estimates unknowns from a series of measurements over time
is the process noise, which is assumed to be drawn from a zero mean multivariate normal distribution, N {\displaystyle {\mathcal {N}}} , with covariance
Kalman_filter
Statistical function that defines the quantiles of a probability distribution
attention on methods based on quantile functions, as they work well with multivariate techniques based on either copula or quasi-Monte-Carlo methods and Monte
Quantile_function
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