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Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
Partial least squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression [1]; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space of maximum ...
The algorithm can be extended to cover slopes between 0 and -1 by checking whether y needs to increase or decrease (i.e. dy < 0) plotLineLow(x0, y0, x1, y1) dx = x1 - x0 dy = y1 - y0 yi = 1 if dy < 0 yi = -1 dy = -dy end if D = (2 * dy) - dx y = y0 for x from x0 to x1 plot(x, y) if D > 0 y = y + yi D = D + (2 * (dy - dx)) else D = D + 2*dy end if
A non-vertical line can be defined by its slope m, and its y-intercept y 0 (the y coordinate of its intersection with the y-axis). In this case, its linear equation can be written = +. If, moreover, the line is not horizontal, it can be defined by its slope and its x-intercept x 0. In this case, its equation can be written
The following version is often seen when considering linear regression. [4] Suppose that (,) is a standard multivariate normal random vector (here denotes the n-by-n identity matrix), and if , …, are all n-by-n symmetric matrices with = =.
In computer graphics, the Liang–Barsky algorithm (named after You-Dong Liang and Brian A. Barsky) is a line clipping algorithm. The Liang–Barsky algorithm uses the parametric equation of a line and inequalities describing the range of the clipping window to determine the intersections between the line and the clip window.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.