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Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
Moreover, Hadamard's inequality provides an upper bound on the absolute values of the intermediate and final entries, and thus a bit complexity of ~ (), using soft O notation. Moreover, as an upper bound on the size of final entries is known, a complexity O ~ ( n 4 ) {\displaystyle {\tilde {O}}(n^{4})} can be obtained with modular computation ...
Here Σ is an n-by-p rectangular diagonal matrix of positive numbers σ (k), called the singular values of X; U is an n-by-n matrix, the columns of which are orthogonal unit vectors of length n called the left singular vectors of X; and W is a p-by-p matrix whose columns are orthogonal unit vectors of length p and called the right singular ...
VOFDM replaces each scalar value in the conventional OFDM by a vector value and is a bridge between OFDM and the single carrier frequency domain equalizer (SC-FDE). When the vector size is 1 {\displaystyle 1} , it is OFDM and when the vector size is at least the channel length and the FFT size is 1 {\displaystyle 1} , it is SC-FDE.
Recursive flood fill with 4 directions. Flood fill, also called seed fill, is a flooding algorithm that determines and alters the area connected to a given node in a multi-dimensional array with some matching attribute.
Reducing the range of any index to a single value effectively eliminates that index. This feature can be used, for example, to extract one-dimensional slices (vectors: in 3D, rows, columns, and tubes [ 1 ] ) or two-dimensional slices (rectangular matrices) from a three-dimensional array.
In the case of support vector machines, a data point is viewed as a -dimensional vector (a list of numbers), and we want to know whether we can separate such points with a ()-dimensional hyperplane. This is called a linear classifier. There are many hyperplanes that might classify the data.