Graph theory | Finite differences | Operator theory | Numerical differential equations | Geometry processing

Discrete Laplace operator

In 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 the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix. The discrete Laplace operator occurs in physics problems such as the Ising model and loop quantum gravity, as well as in the study of discrete dynamical systems. It is also used in numerical analysis as a stand-in for the continuous Laplace operator. Common applications include image processing, where it is known as the Laplace filter, and in machine learning for clustering and semi-supervised learning on neighborhood graphs. (Wikipedia).

Discrete Laplace operator
Video thumbnail

Lecture 18: The Laplace Operator (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Video thumbnail

Differential Equations | The Laplace Transform of a Derivative

We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Laplace Transform

Video thumbnail

Discrete Laplace Equation | Lecture 62 | Numerical Methods for Engineers

Derivation of the discrete Laplace equation using the central difference approximations for the partial derivatives. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscr

From playlist Numerical Methods for Engineers

Video thumbnail

Differential Equations | Laplace Transform of a Piecewise Function

We find the Laplace transform of a piecewise function using the unit step function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Laplace Transform

Video thumbnail

Laplace Transform and Piecewise or Discontinuous Functions

Watch the Intro to the Laplace Transform in my Differential Equations playlist here: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 This video deals particularly with how the Laplace Transform works with piecewise functions, a type of discontinuous functions. T

From playlist Laplace Transforms and Solving ODEs

Video thumbnail

3 Properties of Laplace Transforms: Linearity, Existence, and Inverses

The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions

From playlist Laplace Transforms and Solving ODEs

Video thumbnail

Calculus 3: Divergence and Curl (23 of 32) The Laplace Operator: Ex. 1

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the Laplace operator of f=x^2+y^3+x(y^2)z. Next video in the series can be seen at: https://youtu.be/CSB7G4ueb30

From playlist CALCULUS 3 CH 8 DIVERGENCE AND CURL

Video thumbnail

Introduction to Laplace Transforms

This video introduces the Laplace transform of a function and explains how they are used to solve differential equations. http://mathispower4u.com

From playlist Laplace Transforms

Video thumbnail

Z transform of sampled signals

I explain the maths behind doing a z transform of a sampled signal

From playlist Discrete

Video thumbnail

Dalimil Mazáč - Bootstrapping Automorphic Spectra

I will explain how the conformal bootstrap can be adapted to place rigorous bounds on the spectra of automorphic forms on locally symmetric spaces. A locally symmetric space is of the form H\G/K, where G is a non-compact semisimple Lie group, K the maximal compact subgroup of G, and H a di

From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory

Video thumbnail

Inverting the Z transform and Z transform of systems

I move from signals to systems in describing discrete systems in the z domain

From playlist Discrete

Video thumbnail

Laplace Transform is a Linear Operator - Proof

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Laplace Transform is a Linear Operator - Proof. In this video I quickly prove the important property that the Laplace transform is a linear operator. This say

From playlist The Laplace Transform

Video thumbnail

Benjamin Stamm: A perturbation-method-based post-processing of planewave approximations for

Benjamin Stamm: A perturbation-method-based post-processing of planewave approximations for Density Functional Theory (DFT) models The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Non-local Material Models and Concurrent Multisc

From playlist HIM Lectures: Trimester Program "Multiscale Problems"

Video thumbnail

Lecture 23: Physically Based Animation and PDEs (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

Video thumbnail

Viscosity solutions approach to variational problems - Daniela De Silva

Women and Mathematics: Colloquium Topic: Viscosity solutions approach to variational problems Speaker: Daniela De Silva Affiliation: Columbia University Date: May 21, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Carlos Esteve Yague - Spectral decomposition of atomic structures in heterogeneous cryo-EM

Recorded 18 November 2022. Carlos Esteve-Yague of the University of Cambridge Department of Applied Mathematics and Theoretical Physics presents "Spectral decomposition of atomic structures in heterogeneous cryo-EM" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: In this

From playlist 2022 Cryo-Electron Microscopy and Beyond

Video thumbnail

Bertrand Maury: Mathematics behind some phenomena in crowd motion: Stop and Go waves and...

Abstract: This minicourse aims at providing tentative explanations of some specific phenomena observed in the motion of crowds, or more generally collections of living entities. The first lecture shall focus on the so-called Stop and Go Waves, which sometimes spontaneously emerge and persi

From playlist Mathematical Physics

Video thumbnail

C75 Introduction to the Laplace Transform

Another method of solving differential equations is by firs transforming the equation using the Laplace transform. It is a set of instructions, just like differential and integration. In fact, a function is multiplied by e to the power negative s times t and the improper integral from ze

From playlist Differential Equations

Video thumbnail

"Magnetic Edge and Semiclassical Eigenvalue Asymptotics" by Dr. Ayman Kachmar

What will be the energy levels of an electron moving in a magnetic field? In a typical setting, these are eigenvalues of a special magnetic Laplace operator involving the semiclassical parameter (a very small parameter compared to the sample’s scale), and the foregoing question becomes on

From playlist CAMS Colloquia

Related pages

Schrödinger equation | Graph (discrete mathematics) | Dynkin diagram | ADE classification | Dynamical system | Self-adjoint operator | Lattice (group) | Spectral theorem | Kernel (linear algebra) | Cuboid | Stone space | Cluster analysis | Kronecker delta | Finite volume method | Regular grid | Regular graph | Laplacian matrix | Square lattice | Kronecker sum of discrete Laplacians | Green's function | Gaussian function | Mathematics | Function (mathematics) | Matrix differential equation | Neumann boundary condition | Self-adjoint | Distance (graph theory) | Heat equation | Ring (mathematics) | Sinc function | Discrete calculus | Convolution | Five-point stencil | Manifold | Dirichlet boundary condition | Kronecker product | Numerical analysis | Laplace operator | Finite element method | Ising model | Spectral shape analysis | Discrete exterior calculus | Resolvent formalism | Digital filter | Boolean algebra (structure)