Numerical linear algebra

Iterative refinement

Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations. When solving a linear system due to the compounded accumulation of rounding errors, the computed solution may sometimes deviate from the exact solution Starting with iterative refinement computes a sequence which converges to when certain assumptions are met. (Wikipedia).

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Comparing Iterative and Recursive Factorial Functions

Comparing iterative and recursive factorial functions

From playlist Computer Science

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Recursive Factorial Function

Introduction to recursion.

From playlist Computer Science

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Iterative Fibonacci Function Example

One way to write a Fibonacci function iteratively

From playlist Computer Science

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B22 Introduction to Substitutions

An overview of the three type of substitutions as a new method of solving linear, exact, and "almost" separable differential equations.

From playlist Differential Equations

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The Importance of Atonement

The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and

From playlist RELATIONSHIPS

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What is an Injective Function? Definition and Explanation

An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez

From playlist Functions

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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

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Martin Vohralík: Adaptive inexact Newton methods and their application to multi-phase flows

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 Numerical Analysis and Scientific Computing

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Martin Vohralik: A posteriori error estimates and solver adaptivity in numerical simulations

Abstract: We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic s

From playlist Numerical Analysis and Scientific Computing

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MFEM Workshop 2022 | High-Order Solvers + GPU Acceleration

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s second community workshop was held on October 25, 2022, with participants around the world. Learn more about MFEM at https://mfem.o

From playlist MFEM Community Workshop 2022

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C80 Solving a linear DE with Laplace transformations

Showing how to solve a linear differential equation by way of the Laplace and inverse Laplace transforms. The Laplace transform changes a linear differential equation into an algebraical equation that can be solved with ease. It remains to do the inverse Laplace transform to calculate th

From playlist Differential Equations

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Maria Charina: Algebraic multigrid and subdivision

Abstract: Multigrid is an iterative method for solving large linear systems of equations whose Toeplitz system matrix is positive definite. One of the crucial steps of any Multigrid method is based on multivariate subdivision. We derive sufficient conditions for convergence and optimality

From playlist Numerical Analysis and Scientific Computing

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Predictive Coding Approximates Backprop along Arbitrary Computation Graphs (Paper Explained)

#ai #biology #neuroscience Backpropagation is the workhorse of modern deep learning and a core component of most frameworks, but it has long been known that it is not biologically plausible, driving a divide between neuroscience and machine learning. This paper shows that Predictive Codin

From playlist Papers Explained

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5 Common Scrum Events

Get the most out of the 5 most common Scrum events: - Backlog refinement - Sprint planning - Daily Scrum - Sprint review - Sprint retrospective Video by Agile Coach Chris Gagné: https://chrisgagne.com/ - Learn to code for free and get a developer job: https://www.freecodecamp.com Read

From playlist Tutorials

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6. Szemerédi's graph regularity lemma I: statement and proof

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Szemerédi's graph regularity lemma is a powerful tool in

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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MFEM Workshop 2021 | High-Order Matrix-Free Solvers

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s first community workshop was held virtually on October 20, 2021, with participants around the world. Learn more about MFEM at https

From playlist MFEM Community Workshop 2021

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Olga Mula Hernandez: PinTS cheme using time as a parameter

When thinking about parallel in time schemes, one often tends to view time as a variable to discretize within a numerical scheme (that usually involves a time marching strategy). In this talk, I propose to review alternative strategies where time can be seen as a parameter so that computin

From playlist Jean-Morlet Chair - Gander/Hubert

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Ahmed Ratnani: Towards complex and realistic tokamaks geometries in computational plasma physics

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

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A03 The Esophagus Physiology

Now, a look at the principles of the function of the esophagus

From playlist Acute Care Surgery

Related pages

IEEE 754 | Round-off error | Iterative method | James H. Wilkinson | Cholesky decomposition | Uniform norm | Floating-point arithmetic | Matrix decomposition | Machine epsilon | Condition number | Gaussian elimination | Quadruple-precision floating-point format | Approximation error | Extended precision | LU decomposition