Search results
Results From The WOW.Com Content Network
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.
The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid , though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals .
Multivariate interpolation is the interpolation of functions of more than one variable. Methods include nearest-neighbor interpolation, bilinear interpolation and bicubic interpolation in two dimensions, and trilinear interpolation in three dimensions. They can be applied to gridded or scattered data.
Brahmagupta's interpolation formula — seventh-century formula for quadratic interpolation; Extensions to multiple dimensions: Bilinear interpolation; Trilinear interpolation; Bicubic interpolation; Tricubic interpolation; Padua points — set of points in R 2 with unique polynomial interpolant and minimal growth of Lebesgue constant; Hermite ...
Quadratic profile. For the one-dimensional domain shown in the figure the Φ value at a control volume face is approximated using three-point quadratic function passing through the two bracketing or surrounding nodes and one other node on upstream side. [4]
In the sixth iteration, we cannot use inverse quadratic interpolation because b 5 = b 4. Hence, we use linear interpolation between (a 5, f(a 5)) = (−3.35724, −6.78239) and (b 5, f(b 5)) = (−2.71449, 3.93934). The result is s = −2.95064, which satisfies all the conditions. But since the iterate did not change in the previous step, we ...
An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".