For function values known on a regular grid (having predetermined, not necessarily uniform, spacing), the following methods are available. • Nearest-neighbor interpolation • n-linear interpolation (see bi- and trilinear interpolation and multilinear polynomial) http://www.ag.jku.at/pubs/2012gj.pdf
Approximation with diversified B-splines - ScienceDirect
Webmethod, and tensor product of univariate B-splines or wavelets for 2D FDA to the interested reader. Our approach to FDA in the bivariate setting is a straightforward ap- Since Curve Fitting Toolbox can handle splines with vectorcoefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines. Most spline construction commands in the toolbox take advantage of this. However, you might be interested in seeing a detailed description … See more Consider, for example, least-squares approximation to given data z(i,j) = f(x(i),y(j)) for i = 1:I, j = 1:J. Here are some gridded data, taken … See more Next, we choose a spline order ky and a knot sequence knotsyfor the y-direction and then obtain a spline curve whose i-th component is an … See more Note that the statements [xx,yy] = ndgrid(x,y); z = franke(xx,yy); used above make certain that z(i,j) is the value of the function being … See more In particular, creates the matrix vals whose (i,j)-th element can be taken as an approximation to the value f(x(i),yy(j)) of the underlying function f at the grid point (x(i),yy(j)). This is evident when we plot vals. Note that, for … See more duties as a husband
Bases and dimensions of bivariate hierarchical tensor–product …
WebThe focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate ... WebSep 3, 2024 · Looking at spap2 it is the least-squares spline approximation method so it is an approximation. Increasing the number of knots will improve the approximation at the cost of producing a more complex curve. Consider adding more knot values between x = 0 and 0.01 to reduce this error and provide a better result. Let me know if this helps, Christopher WebNov 22, 2010 · Bivariate smoothing has been studied in the literature, such as bivariate P-splines (Eilers and Marx, 2003;Marx and Eilers, 2005), bivariate tensor product P … duties as a sales associate