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A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
Linear extrapolation means creating a tangent line at the end of the known data and extending it beyond that limit. Linear extrapolation will only provide good results when used to extend the graph of an approximately linear function or not too far beyond the known data.
Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the matrix A. The approximate solution is realized as an exact solution to A x = b', where b' is the projection of b onto the column space of A. The best ...
Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions. The further the extrapolation goes outside the data, the more room there is for the model to fail due to differences between the assumptions and the sample data or the true values.
Linear-fractional programming — objective is ratio of linear functions, constraints are linear Fractional programming — objective is ratio of nonlinear functions, constraints are linear; Nonlinear complementarity problem (NCP) — find x such that x ≥ 0, f(x) ≥ 0 and x T f(x) = 0; Least squares — the objective function is a sum of squares
IRLS can be used for ℓ 1 minimization and smoothed ℓ p minimization, p < 1, in compressed sensing problems. It has been proved that the algorithm has a linear rate of convergence for ℓ 1 norm and superlinear for ℓ t with t < 1, under the restricted isometry property, which is generally a sufficient condition for sparse solutions.
Triangulated irregular network-based linear interpolation (a type of piecewise linear function) n-simplex (e.g. tetrahedron) interpolation (see barycentric coordinate system) Inverse distance weighting; ABOS - approximation based on smoothing; Kriging; Gradient-enhanced kriging (GEK) Thin plate spline
XLfit is a Microsoft Excel add-in that can perform regression analysis, curve fitting, and statistical analysis. It is approved by the UK National Physical Laboratory and the US National Institute of Standards and Technology [1] XLfit can generate 2D and 3D graphs and analyze data sets. XLfit can also analyse the statistical data.