The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation. This is often referred to as the all-electron full-potential linearized augmented-plane-wave method (FLAPW). It does not rely on the pseudopotential approximation and employs a systematically extendable basis set. These features make it one of the most precise implementations of DFT, applicable to all crystalline materials, regardless of their chemical composition. It can be used as a reference for evaluating other approaches. (Wikipedia).
Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.
From playlist Linear Algebra
C34 Expanding this method to higher order linear differential equations
I this video I expand the method of the variation of parameters to higher-order (higher than two), linear ODE's.
From playlist Differential Equations
Francois Gygi - Generating Reference Data and Controlling Accuracy in DFT and Hybrid DFT Simulations
Recorded 03 May 2022. Francois Gygi of University of California, Davis, Computer Science, presents "Generating Reference Data and Controlling Accuracy in DFT and Hybrid DFT Simulations" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: Density Funct
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Use linear algebra for equation of planes and lines.
From playlist Linear Algebra
Using linear algebra to solve for equation of lines and planes.
From playlist Linear Algebra
What Sparsity and l1 Optimization Can Do For You
Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations. l1 and related optimization solvers are a key tool in this area. The special nature o
From playlist Complete lectures and talks: slides and audio
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Using linear algebra to solve for equations of lines and planes.
From playlist Linear Algebra
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Colin Ophus - Multi-dimensional scanning transmission electron microscopy to solve 3D nanostructures
Recorded 24 October 2022. Colin Ophus of Lawrence Berkeley Laboratory presents "Using multi-dimensional scanning transmission electron microscopy to solve 3D nanostructures using atomic electron tomography" at IPAM's Mathematical Advances for Multi-Dimensional Microscopy Workshop. Abstract
From playlist 2022 Mathematical Advances for Multi-Dimensional Microscopy
Michael Unser - High-Speed Fourier Ptychography with Deep Spatio-Temporal Priors - IPAM at UCLA
Recorded 11 October 2022. Michael Unser of the École Polytechnique Fédérale de Lausanne (EPFL) Biomedical Imaging Group presents "High-Speed Fourier Ptychography with Deep Spatio-Temporal Priors" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: Fourier ptychography (F
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Benjamin Stamm - Eigenvalue problems and error control - IPAM at UCLA
Recorded 10 March 2022. Benjamin Stamm of RWTH Aachen University presents "Eigenvalue problems and error control" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/advancing-quantum-mechanics-w
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Patrick Joly: Long time behaviour of the solution of Maxwell’s equations in dissipative Lorentz...
CONFERENCE Recorded during the meeting " Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials " the May 25, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video a
From playlist Numerical Analysis and Scientific Computing
WildLinAlg14: More row reduction with parameters
This video explains the second half of row reduction, a basic algorithm in linear algebra used to solve systems of linear equations. Parameters are introduced corresponding to non-leading columns of the augmented matrix of the system. This is the 14th lecture of this course on Linear Al
From playlist A first course in Linear Algebra - N J Wildberger
3 Nandakumaran - An Introduction to deterministic optimal control and controllability
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Daniel Kral: Parametrized approach to block structured integer programs
Integer programming is one of the most fundamental problems in discrete optimization. While integer programming is computationally hard in general, there exist efficient algorithms for special instances. In particular, integer programming is fixed parameter tractable when parameterized by
From playlist Workshop: Parametrized complexity and discrete optimization
AMMI Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract group
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations