Hierarchical Interpolative Factorization
Offered By: Society for Industrial and Applied Mathematics via YouTube
Course Description
Overview
Explore recent developments in matrix factorization techniques for discretized differential and integral operators in this 33-minute conference talk from the 2013 SIAM Annual Meeting. Delve into the innovative use of interpolative decomposition for numerically low-rank matrices, and discover efficient algorithms for applying and inverting these operators. Follow the presentation as it covers problem statements, notations, Schur complement, skeletonization, and hierarchical interpolative factorization methods for both differential and integral equations in 2D and 3D contexts. Gain insights into nested dissection, DSRS, and practical examples that demonstrate the application of these advanced mathematical concepts.
Syllabus
Intro
Problem statement
Notations and tools
Schur complement
Interpolative decomposition (ID)
Skeletonization
Differential equation (DE)
2D nested dissection (level 0)
2D HIF-DE (level 0.5)
2D HIF-DE (Example)
3D nested dissection
3D HIF-DE (example)
Integral equation
2D DSRS (level 0)
2D DSRS (level 1)
2D HIF-IE (level 0.5)
2D HIF-IE (example)
3D HIF-IE (example)
Conclusions
Taught by
Society for Industrial and Applied Mathematics
Related Courses
Scientific ComputingUniversity of Washington via Coursera Differential Equations in Action
Udacity Initiation à la théorie des distributions
École Polytechnique via Coursera Everything is the Same: Modeling Engineered Systems
Northwestern University via Coursera Analyse numérique pour ingénieurs
École Polytechnique Fédérale de Lausanne via Coursera