mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating the negative continuous Laplacian obtained...

In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean...

mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place...

_{i}^{2}u(x)} . The discrete Laplace operator Δ h u {\displaystyle \Delta _{h}u} depends on the dimension n {\displaystyle n} . In 1D the Laplace operator is approximated...

automaton Discrete differential geometry Discrete Laplace operator Calculus of finite differences, discrete calculus or discrete analysis Discrete Morse theory...

eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under...

Laplacian vector field Laplace's equation Laplace operator Discrete Laplace operator Laplace–Beltrami operator Laplacian, see Laplace operator Infinity Laplacian...

combinatorics. Topics in this area include: Discrete Laplace operator Discrete exterior calculus Discrete calculus Discrete Morse theory Topological combinatorics...

vision) Feature extraction Discrete Laplace operator Prewitt operator Irwin Sobel, 2014, History and Definition of the Sobel Operator K. Engel (2006). Real-time...

geometry processing and topological combinatorics. Discrete Laplace operator Discrete exterior calculus Discrete Morse theory Topological combinatorics Spectral...

In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable...

formulating discrete operators on graphs which are analogous to differential operators in calculus, such as graph Laplacians (or discrete Laplace operators) as...

partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that...

or (increasingly) of the graph's Laplacian matrix due to its discrete Laplace operator, which is either D − A {\displaystyle D-A} (sometimes called the...

differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement...

functions may have a nowhere continuous convolution. In the discrete case, the difference operator D f(n) = f(n + 1) − f(n) satisfies an analogous relationship:...

integral operator Jacobi transform Laguerre transform Laplace transform Inverse Laplace transform Two-sided Laplace transform Inverse two-sided Laplace transform...

mathematics, the infinity Laplace (or L ∞ {\displaystyle L^{\infty }} -Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated...

transfer function, which is the Laplace transform of the system's impulse response (or Z transform in the case of discrete-time systems). As a result of...

– aperiodic signals, transients. Laplace transform – electronic circuits and control systems. Z transform – discrete-time signals, digital signal processing...

fact. Ladder operators then become ubiquitous in quantum mechanics from the angular momentum operator, to coherent states and to discrete magnetic translation...

In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle...

more noticeable in their viewing conditions.[citation needed] Discrete Laplace operator Acutance admin. "You should now turn down the sharpness of your...

Prewitt operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing...

}}(A-zI)^{-1}~dz} defines a projection operator onto the λ eigenspace of A. The Hille–Yosida theorem relates the resolvent through a Laplace transform to an integral...

However, they do admit a Laplace domain description, with identical half-planes of convergence in the complex plane (or in the discrete case, the Z-plane),...

eigenvalues of discrete Laplace operator Kronecker sum of discrete Laplacians — used for Laplace operator in multiple dimensions Discrete Poisson equation...

\nabla ^{2}} . In three dimensions using Cartesian coordinates the Laplace operator is ∇ 2 = ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 + ∂ 2 ∂ z 2 {\displaystyle \nabla ^{2}={\frac...