Geometric algorithms | Optimization algorithms and methods
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. In this setting, the mean operation is an integral over a region of space, and the nearest centroid operation results in Voronoi diagrams. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd's algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantization, dithering, and stippling. Other applications of Lloyd's algorithm include smoothing of triangle meshes in the finite element method. (Wikipedia).
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
The Fast Fourier Transform Algorithm
Here I discuss the Fast Fourier Transform (FFT) algorithm, one of the most important algorithms of all time. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter 2 from: "Data-Driven Science and Engineering: Machine Learning, D
From playlist Fourier
Gaussian Integral 6 Gamma Function
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using properties of the gamma function, which
From playlist Gaussian Integral
This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won
From playlist Differential equations
The Fast Fourier Transform (FFT)
Here I introduce the Fast Fourier Transform (FFT), which is how we compute the Fourier Transform on a computer. The FFT is one of the most important algorithms of all time. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter
From playlist Fourier
The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
In this video, we take a look at one of the most beautiful algorithms ever created: the Fast Fourier Transform (FFT). This is a tricky algorithm to understand so we take a look at it in a context that we are all familiar with: polynomial multiplication. You will see how the core ideas of t
From playlist Fourier
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
CS50 Explained 2016 - Week 0 - Finding Mike Smith
This is CS50 Explained, wherein David J. Malan and Doug Lloyd watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 0's lecture, see https://www.youtube.com/watch?v=o4SGkB_8fFs.
From playlist CS50 Explained 2016
CS50 Explained VR 2016 - Week 0 - Finding Mike Smith
This is CS50 Explained VR, wherein David J. Malan and Doug Lloyd (and you!) watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 0's lecture, see https://www.youtube.com/watch?v=0C8a6GBF8Bg.
From playlist CS50 Explained 2016 in Virtual Reality
How to Come Up with the Semi-Implicit Euler Method Using Hamiltonian Mechanics #some2 #PaCE1
Notes for this video: https://josephmellor.xyz/downloads/symplectic-integrator-work.pdf When you first learn about Hamiltonian Mechanics, it seems like Lagrangian Mechanics with more work for less gain. The only reason we even learn Hamiltonian Mechanics in undergrad is that the Hamiltoni
From playlist Summer of Math Exposition 2 videos
CS50 Explained 2016 - Week 3 - Merge Sort
This is CS50 Explained, wherein David J. Malan and Doug Lloyd watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 3's lecture, see https://www.youtube.com/watch?v=jUyQqLvg8Qw.
From playlist CS50 Explained 2016
CS50 Explained VR 2016 - Week 3 - Merge Sort
This is CS50 Explained VR, wherein David J. Malan and Doug Lloyd (and you!) watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 3's lecture, see https://www.youtube.com/watch?v=t_gxXV3s04I.
From playlist CS50 Explained 2016 in Virtual Reality
CS50 Explained 2016 - Week 3 - Sorting Humans
This is CS50 Explained, wherein David J. Malan and Doug Lloyd watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 3's lecture, see https://www.youtube.com/watch?v=jUyQqLvg8Qw.
From playlist CS50 Explained 2016
CS50 Explained VR 2016 - Week 3 - Sorting Humans
This is CS50 Explained VR, wherein David J. Malan and Doug Lloyd (and you!) watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 3's lecture, see https://www.youtube.com/watch?v=t_gxXV3s04I.
From playlist CS50 Explained 2016 in Virtual Reality
CS50 Explained 2016 - Week 0 - Taking Attendance
This is CS50 Explained, wherein David J. Malan and Doug Lloyd watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 0's lecture, see https://www.youtube.com/watch?v=o4SGkB_8fFs.
From playlist CS50 Explained 2016
CS50 Explained VR 2016 - Week 0 - Taking Attendance
This is CS50 Explained VR, wherein David J. Malan and Doug Lloyd (and you!) watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 0's lecture, see https://www.youtube.com/watch?v=0C8a6GBF8Bg.
From playlist CS50 Explained 2016 in Virtual Reality
Quantum Simulations I by Barry Sanders
Dates: Thursday 03 Jan, 2013 - Saturday 05 Jan, 2013 Venue: ICTS-TIFR, IISc Campus, Bangalore The school aims to provide students and researchers an introduction to the field of quantum information, computation and communication. Topics that will be covered include introduction to quantu
From playlist Mini Winter School on Quantum Information and Computation
B03 An improvement of the Euler method
Introducing predictor-corrector methods, improving on Euler's method of numerical analysis.
From playlist A Second Course in Differential Equations
CS50 Explained 2016 - Week 3 - Finding 50
This is CS50 Explained, wherein David J. Malan and Doug Lloyd watch CS50's lectures and discuss the pedagogy behind CS50 itself. For Week 3's lecture, see https://www.youtube.com/watch?v=jUyQqLvg8Qw.
From playlist CS50 Explained 2016