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Image derivatives can be computed by using small convolution filters of size 2 × 2 or 3 × 3, such as the Laplacian, Sobel, Roberts and Prewitt operators. [1] However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives [2] and Gabor filters. [3]
Finite Difference Approach to Option Pricing (includes Matlab Code); Numerical Solution of Black–Scholes Equation, Tom Coleman, Cornell University; Option Pricing – Finite Difference Methods, Dr. Phil Goddard; Numerically Solving PDE’s: Crank-Nicolson Algorithm, Prof. R. Jones, Simon Fraser University
The higher-order derivatives are less common than the first three; [1] [2] thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics and is implemented in MATLAB. [3] The fourth derivative is referred to as snap, leading the fifth and sixth derivatives to be "sometimes somewhat ...
Differential quadrature is the approximation of derivatives by using weighted sums of function values. [22] [23] Differential quadrature is of practical interest because its allows one to compute derivatives from noisy data.
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 (+) + (() +).
The Prewitt operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function.
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".
The secant method can be interpreted as a method in which the derivative is replaced by an approximation and is thus a quasi-Newton method. If we compare Newton's method with the secant method, we see that Newton's method converges faster (order 2 against order the golden ratio φ ≈ 1.6). [2]