Given a set of data and the desire to produce some kind of model of those data, there are a variety of functions that can be chosen for the fit. If there is no prior understanding of the data, then th ...
A simple example of a quadratic spline (a spline of degree 2) isS(t) = \begin{cases}(t+1)^2-1 -2 \le t 0\\1-(t-1)^2 0 \le t \le 2\end{cases}for which S'(0)=2.A simple example of a cubic spline isS( ...
Related terms and techniques -The basic idea of Kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood o ...
The expected result is a discrete assignment of the unknown function u in a study region:u(x): x \rightarrow \mathbb{R}, \quad x \in \mathbf{D} \sub \mathbb{R}^nwhere \mathbf{D} is the study region.Th ...
A weighted average is any average that has multiplying factors to give different weights to data at different positions in the sample window. Mathematically, the moving average is the convolution of t ...
Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricin ...
In the simplest and most familiar case (shown in the first picture), we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point and its corres ...
A triangulated irregular network (TIN) is a digital data structure used in a geographic information system (GIS) for the representation of a surface. A TIN is a vector-based representation of the phys ...
For example, suppose we have a table like this, which gives some values of an unknown function f.Plot of the data points as given in the table.x f(x)0 01 0 . 84152 0 . 90933 0 . 14114 ?0 . 7568 ...
There are several methods to render matrices into a more easily accessible form. They are generally referred to as matrix decomposition or matrix factorization techniques. The interest of all these te ...
A matrix is a rectangular array of numbers or other mathematical objects, for which operations such as addition and multiplication are defined. Most commonly, a matrix over a field F is a rectangular ...
Map algebra is a set-based algebra for manipulating geographic data, proposed by Dr. Dana Tomlin in the early 1980s. It is a set of primitive operations in a geographic information system (GIS) which ...
The symmetric difference is equivalent to the union of both relative complements, that is:A\,\triangle\,B = (A \smallsetminus B) \cup (B \smallsetminus A),\,and it can also be expressed as the union o ...
The intersection of A and B is written "A ∩ B". Formally:A \cap B = \{ x: x \in A \,\land\, x \in B\}that isx ∈ A ∩ B if and only ifx ∈ A andx ∈ B.For example:The intersection of the sets {1, 2, ...
The union of two sets A and B is the collection of points which are in A or in B or in both A and B. In symbols,A \cup B = \{ x: x \in A \,\,\,\textrm{ or }\,\,\, x \in B\}.For example, if A = {1, 3, ...
