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In OpenMDAO terms, your nonlinear system is your model or governing system of equations. Your linear system is a behind-the-scenes linearization of your model used for computing derivatives. You need to use a nonlinear solver when there's backwards coupling or implicit systems; you need to use linear solver when using derivatives for Newton solvers or optimizers. 0:00 - Intro 2:00 - What are nonlinear and linear systems? 8:11 - Differences between nonlinear and linear solvers 11:52 - Conclusion Accompanying notebook: 🤍 TODO: add linked lectures as they're developed The referenced textbook Engineering Design Optimization by Martins and Ning is available for free at 🤍
This talk will describe how the JuMP and HiGHS teams have worked together to deliver the best open-source linear optimization solvers to the Julia community, and present some high-profile use cases. For more info on the Julia Programming Language, follow us on Twitter: 🤍 and consider sponsoring us on GitHub: 🤍 00:00 Welcome! 00:10 Help us add time stamps or captions to this video! See the description for details. Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: 🤍 Interested in improving the auto generated captions? Get involved here: 🤍
This talk focuses on challenges that we address when designing linear solvers that aim at achieving scalability on large scale computers, while also preserving numerical robustness. We will consider preconditioned Krylov subspace solvers. Getting scalability relies on reducing global synchronizations between processors, while also increasing the arithmetic intensity on one processor. Achieving robustness relies on ensuring that the condition number of the preconditioned matrix is bounded. We will discuss two different approaches for this. The first approach relies on enlarged Krylov subspace methods that aim at computing an enlarged subspace and obtain a faster convergence of the iterative method. The second approach relies on a multilevel Schwarz preconditioner, a multilevel extension of the GenEO preconditioner, that is basedon constructing robustly a hierarchy of coarse spaces. Numerical results on large scale computers, in particular for linear systems arising from solving linear elasticity problems, will discuss the efficiency of the proposed methods. Recording during the meeting Parallel Solution Methods for Systems Arising from PDEs" the September 18, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: 🤍. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
Finish off with the discussion on errors and start discussion on linear solvers and linear systems of equations
Presented at the Argonne Training Program on Extreme-Scale Computing 2017. Slides for this presentation are available here: 🤍
Slides for this presentation can be viewed here: 🤍 Presented at the Argonne Training Program on Extreme-Scale Computing, Summer 2014. For more information, visit: 🤍
Slides for this presentation are available here: 🤍 Presented at the Argonne Training Program on Extreme-Scale Computing, Summer 2015. For more information on the Argonne Training Program on Extreme-Scale Computing, visit: 🤍
Solving linear systems is a key component of beamforming applications such as audio, radar, and wireless communication. Learn about the matrix factorization and linear system solver blocks from Fixed-Point Designer™. This block set can perform bit and cycle accurate simulation as well as generate efficient HDL code. Users can also choose different architectures to optimize for high throughput or low hardware utilization. Get a free product trial: 🤍 Learn more about MATLAB: 🤍 Learn more about Simulink: 🤍 See what's new in MATLAB and Simulink: 🤍 © 2022 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See 🤍mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.
EuroTUG 2022: Trilinos Linear Solvers and Preconditioners- Overview and New Capabilities (How to choose a Belos Krylov Solver; MueLu updates and new research efforts) Presenters: Jennifer Loe and Graham Harper- Sandia National Laboratories Slides can be found here: 🤍 Find more information at the EuroTUG website: 🤍
Continue discussion on linear solvers. Introduce the challenges faced by direct methods. Introduce tridiagonal-systems and the Thomas or Tridiagonal Matrix Algorithm (TDMA). Discuss heat transfer problem
Discuss iterative solvers, Jacobi, Gauss-Seidel, and Successive Over Relaxation (SOR)
#excel #solver #linearprogramming Please SUBSCRIBE: 🤍 🤍 Please watch: "Linear Programming Optimization Transportation Problem Excel Solver" 🤍 A tablet computer manufacturer offers two models of its product, the Tablet Pro and the Tablet Mini. The Tablet Pro requires 1 chipset, 15 electronic components and 6 hours of labor and returns a profit of $182. The Tablet Mini requires 1 chipset, 9hours of labor and 10 electronic components and returns a profit of $139. Monthly resources are limited to 1,000 chipsets, 7,000 labor hours and 14,000 electronic components. The tablet manufacturer is interested in maximizing monthly profit. What product mix achieves maximal profit? Overview of formulating linear programming models and using Solver to find an optimal solution. Includes discussion of sensitivity reports and important terminology. Demonstration of classic two product profit maximization formulation. Spreadsheet used in the video can be downloaded from: 🤍
Modified version of a research talk given at the Copper Mountain Conference on Iterative Methods in Spring 2022. The main idea of this thrust of research is to use weighted probability distributions to allow the parallel algorithm to greedily select the next component to update and to dynamically update that weighting over the course of the iteration.
Choosing the right solver for different finite element simulations can be an advanced step, but after seeing the effect it can have on the execution time and the performance of the simulation, you find out that it’s necessary to know a bit more about it. In this video, we discuss a little bit about various available solvers in FreeFEM, including PETSc with which we have access to tremendous number of tools, solvers, and preconditioners to solve the derived linear system more efficiently. Codes, models, and resources: You can find all the codes and models required to follow the videos and reproduce the output, grouped for different episodes, at 🤍 and 🤍 💡 Finite element series, in which a single problem was solved in different open-source tools including FreeFEM 🤍 💡 Applied numerical computing series, in which the underlying theories of these videos are discussed: 🤍 Topics covered: 🎯 Using MUMPS and UMFPACK solvers in FreeFEM 🎯 PETSc preconditioners and iterative solvers 🎯 Solvers in the sequential and parallel versions of FreeFEM 🎯 Techniques to measure the execution time of simulations Lecturer: Mojtaba Barzegari 🤍 To learn more about the goals of the TuxRiders project, please visit our website at 🤍. Chapters in this video! ################ 00:00 - Intro 00:57 - The base diffusion (Poisson) problem 04:16 - Preparing mesh to check other solvers 06:24 - UMFPACK 09:49 - MUMPS 13:39 - PETSc
Presented at the Argonne Training Program on Extreme-Scale Computing, Summer 2016. Slides for this presentation are available here: 🤍 For more information on the Argonne Training Program on Extreme-Scale Computing, visit: 🤍
Presented at the Argonne Training Program on Extreme-Scale Computing 2018. Slides for this presentation are available here: 🤍
This video was made as an assignment at IIT Bombay
Large-scale computations on networks and graphs arise in many areas of modern data science. Graph theory and linear algebra are of course intimately linked. This minisymposium will highlight tools from sparse matrix computation that are being used to develop efficient implementations of graph algorithms. Such tools range from linear algebra over semirings to fast solvers for Laplacian linear systems. In the former area, matrices over various semirings describe the kernels of a wide variety of graph algorithms in theory, and efficient software for sparse semiring algebra has led to practical, scalable implementations with significant impact. In the latter area, the so-called Laplacian paradigm has lately challenged or replaced the asymptotically best algorithms known for such classic network problems as multicommodity flow, and we anticipate that fast Laplacian solvers will become a standard building block for graph and network software. The minisymposium will open with two talks on sparse semirings for graph computation, the first on theory and the second on efficient implementation and software. The last two talks will highlight current work in graph Laplacians and their applications, and describe a number of applications of the linear algebraic approach to graph computation. This minisymposium is organized under the auspices of the SIAM Activity Group on Applied and Computational Discrete Algorithms. Organizer: John R. Gilbert University of California, Santa Barbara, U.S. Jeremy Kepner Massachusetts Institute of Technology, U.S. SIAM Conference on Mathematics of Data Science (MDS20) MS142 Linear Algebraic Tools for Graph Computation Session 3 Richard Peng, Georgia Institute of Technology, U.S.
An easy video to learn using Microsoft Excel Solver for Linear Programming
Introduction to linear solvers, why they are needed, how to solve systems of equations in Python using numpy. Types of matrices and why direct linear solvers can be so expensive.
This video tutorial provides a basic introduction into the solver tool found in excel. It explains how to use it in solving systems of linear equations in algebra. Excel Tutorial Playlist: 🤍 YouTube Channel Growth Accelerator: 🤍 Algebra For Beginners: 🤍 Excel Tutorial For Beginners: 🤍 Top 30 Excel Tips & Shortcuts: 🤍 How To Calculate Loan Payments In Excel: 🤍 How To Create an Amortization Table: 🤍 How To Make a Line Chart In Excel: 🤍 Split Text Into Multiple Columns In Excel: 🤍 Lock Cells and Protect Sheets In Excel: 🤍 Excel Interactive Checklist: 🤍 Excel Solver Tool - System of Equations: 🤍 Excel Map Charts: 🤍 Excel Pivot Tables: 🤍 Calculate The Total Hours Worked In Excel: 🤍 How To Make a Time-Sheet In Excel: 🤍 Excel - Business Account Ledger: 🤍 Excel Calendars: 🤍 Merge Data From Multiple Columns In Excel: 🤍 Excel Find and Replace Tutorial: 🤍 Resize Multiple Rows and Columns: 🤍 Excel Conditional Formatting: 🤍 How To Move Columns: 🤍 Solving Polynomial Equations - Goal Seek: 🤍 Multiple Dependent Drop Down Lists: 🤍 How To Create a Data Entry Form In Excel: 🤍 Excel Scatter Charts: 🤍 Excel Vlookup Function: 🤍 Excel - Statistics: 🤍 Basic Math Operations In Excel: 🤍 How To Freeze Rows and Columns: 🤍 How To Show & Hide Formulas: 🤍 Excel Pie Charts: 🤍 Excel Bar Graphs: 🤍 How To Use Hyperlinks In Excel: 🤍 Relative & Absolute Cell References: 🤍 Excel Flash Fill: 🤍 Excel Auto Fill: 🤍 Excel Tutors: 🤍 Useful Textbooks: 🤍 Access Premium Videos: 🤍 Organic Chemistry Tutor - Playlists: 🤍 Subscribe To My YouTube Channel: 🤍 E-Book & E-mail Newsletter: 🤍 Affiliate Marketing Disclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
2016 PyLith Tutorial Session V: Optimizing Solver Parameters - Linear Solver - Using PETScSolvers in PyLith Instructors: Brad Aagaard, Charles Williams, Mathew Knepley Download Slides: 🤍
Join 400,000+ professionals in our courses: 🤍 Excel’s Solver tool is an optimization package. It finds the optimal solution to a problem by changing multiple variables. It can solve for more complex “what-if-analysis” which Goal Seek can’t. Goal seek is restricted to changing one variable, whereas with solver you can have many variables. ★ My Online Excel Courses ► 🤍 00:00 Define and Solve a Problem by Using Excel Solver 00:15 Solve Problems in Excel with 2 or More Variables 06:56 Solve What-If Problems with Constraints ► Download the workbook here: 🤍 Calling Solver an “advanced goal seek” doesn’t do it any justice. Solver can handle complex data models and solve for the optimal solution. But; it can also easily solve for the more simpler problems that we might face at work. In this video, I show you two examples: 1 - How to set income to a specific value by changing prices which adding constraints for the price and also full rounded number for units sold. 2. Distribute the remaining budget dollars among your different projects based on certain cost constraints. Goal Seek Video: 🤍 ✉ Subscribe & get my TOP 10 Excel formulas e-book for free 🤍 Get Office 365: 🤍 Microsoft Surface: 🤍 RESOURCES I Recommend: 🤍 More resources on my Amazon page: 🤍 Let’s connect on social: Instagram: 🤍 Twitter: 🤍 LinkedIn: 🤍 Note: This description contains affiliate links, which means at no additional cost to you, we will receive a small commission if you make a purchase using the links. This helps support the channel and allows us to continue to make videos like this. Thank you for your support! #excel
Presented at the Argonne Training Program on Extreme-Scale Computing 2019. Slides for this presentation are available here: 🤍
Low Precision Computing in Sparse Linear Solvers Kengo Nakajima (Information Technology Center, The University of Tokyo) * SC20 Playlists 🤍 * SC20 Website(Information Technology Center, University of Tokyo) 🤍
Continue discussion on Thomas/TDMA and solve the heat equation together in class in Python using the Thomas/TDMA algorithm
Jan Ackmann (U. Oxford) - Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows Virtual Workshop on New Opportunities in ML/AI for Weather and Climate Modelling Session 3 – High performance, Infrastructure and Big data challenges (March 18th) Organised jointly by the H2020 projects IS-ENES3 and ESiWACE2, the workshop was held virtually from the 16th to 18th March 2021. The aim of this workshop was to bring together climate scientists and experts from academia and industry to share knowledge and experience and to identify new opportunities in the areas of machine learning, artificial intelligence and big data techniques for Weather and Climate Modelling. Find the full agenda and download the presentations here: 🤍
Current applications in Computational and Data Science often require the solution of large and sparse linear systems. The notion of "large" is qualitative and there is a clear tendency to increase it; currently, needing to solve systems with millions or even billions of unknowns is not unusual. To efficiently solve the above systems on high-end massively parallel computers, the methods of choice are the Krylov methods, whose convergence and scalability properties are related to the choice of suitable preconditioning techniques. Organized by the EoCoE European Center of Excellence, this webinar was given by Pasqua D'Ambra, senior researcher at CNR (Italy) Official EoCoE website: 🤍 Pasqua D'Ambra page: 🤍
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![[FreeFEM 9] Solvers and preconditioners for the linear system of equations: PETSc, MUMPS, & UMFPACK](https://i.ytimg.com/vi/wGYez2-3rvk/mqdefault.jpg "[FreeFEM 9] Solvers and preconditioners for the linear system of equations: PETSc, MUMPS, & UMFPACK")
