Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
Robert Seiringer: The local density approximation in density functional theory
We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum st
From playlist Mathematical Physics
Linear Approximations and Differentials
Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my
From playlist Partial Derivatives
This video illustrates the importance of antialiasing in 3D content. This video has the same 14-second scene rendered 4 times with different settings each time. Pay attention to the annotations. It is rendered with POV-Ray, but the technique is similar to mipmapping / anisotropic filte
From playlist Misc. productions
Alberto Del Pia: Proximity in concave integer quadratic programming
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n∆ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, n is the number of variables and ∆ denotes the maximum of the absolute va
From playlist Workshop: Tropical geometry and the geometry of linear programming
Lecture with Ole Christensen. Kapitler: 00:00 - Intro To Approximation Theory; 10:00 - Remarks On Vectorspaces In Mat4; 13:30 - Def.: Dense Subset; 19:15 - Dense Subspace Of The Sequence Spaces L^p; 24:45 - Dense Subspace Of The Function Spaces L^p; 35:15 - Weierstrass Approximation Theore
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Les 10 ans du Groupe Calcul - Martin Gander, Université de Genève
Martin Gander, Université de Genève "Gauss, Jacobi, Seidel, Richardson, Krylov : the Invention of Iterative Methods" The invention of iterative methods for systems of linear equations now spans almost two centuries. These methods were invented for the same reasons as they are used today,
From playlist Les 10 ans du Groupe Calcul
Portal 2 Co-op solution for: mp_coop_paint_red_racer
This video shows approximately how I and my friend first solved this stage of Portal 2 Co-operative challenge. I uploaded it, because from what I have seen, everyone solved this stage differently. One more solution cannot hurt. (Quirky movements & execution in general is because I played
From playlist Misc. video game videos
Probability 101c: Stirling's approximation
(C) 2012 David Liao lookatphysics.com CC-BY-SA Replaces unscripted drafts Approximation for n! when n is large Comparison with integral of natural logarithm
From playlist Probability, statistics, and stochastic processes
Mod-01 Lec-02 Polynomial Approximation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Emmanuel Frénod: The geometrical gyro-kinetic approximation
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Physics
Minimax Approximation and the Exchange Algorithm
In this video we'll discuss minimax approximation. This is a method of approximating functions by minimisation of the infinity (uniform) norm. The exchange algorithm is an iterative method of finding the approximation which minimises the infinity norm. FAQ : How do you make these animatio
From playlist Approximation Theory
Finished the Lanczos method, moving onto DMRG on Monday! -- Watch live at https://www.twitch.tv/simuleios
From playlist DMRG
Chrono Cross beginning demo. Captured using pSX, a PSX emulator. This was an interesting technical exercise, because the console uses four different resolutions and two different bitdepths in this span: 256x240, 320x240, 640x240, 640x480, and 15bpp and 32bpp. I implemented lanczos
From playlist Misc. video game videos
Half-Life 2 in low resolution [320x240]
No, I did not make it 256 colors, but I did try out as an experiment how Half-Life 2 would look like at 320x240, a very low resolution by today's standard but once rather standard for gaming. There is no point to this video except to show how it looks like at 320x240. One may immediately n
From playlist Recommended picks
Portal 2 SP Challenges [Smooth Jazz - 1 portal] 256 colors
Portal 2 challenge mode map "smooth jazz" solved with 1 portal and 256 colors in 424x240 resolution. My computer is slow, and the challenge mode does not allow recording with host_timescale, so some scripted elements (such as the lift ride) are jerky. In particular, I did _not_ walk throu
From playlist Portal & Portal 2
Ancient machine (POV-Ray animation, HD & HDRI)
This is a visual inspiration about a music soundtrack in Final Fantasy V. I did not add any sound effects; the audio is verbatim from the game's background music. I modelled and rendered this using POV-Ray, postprocessed using EXR-Utils and PFSTools, in particular using the pfstmo_fattal0
From playlist Misc. productions
Portal 2 SP Challenges [Column Blocker - 4 portals] 256 colors
Portal 2 challenge mode map "column blocker" solved with 4 portals and 256 colors in 424x240 resolution. My computer is slow, and the challenge mode does not allow recording with host_timescale, so the scripted elements (including the movement of the cube when moved around) are jerky. I
From playlist Portal & Portal 2
The Lp Norm for Vectors and Functions
In this video, we expand on the idea of L1 and L2 norms, introduced in the previous video to the more general Lp norm. We will get explain how the norms are calculated and try to get an intuition of the differences between the different Lp norms. Chapters 0:00 - Introduction 1:15 - Lp No
From playlist Approximation Theory
Portal 2 SP Challenges [Incinerator - 5 portals] 256 colors
Portal 2 challenge mode map "incinerator" solved with 5 portals and 256 colors in 424x240 resolution. My computer is slow, and the challenge mode does not allow recording with host_timescale, so the scripted elements (the fall in the beginning; the cubes dropping for incineration, and the
From playlist Portal & Portal 2