An algebraic sparsified nested dissection algorithm using low-rank approximations
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite
linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection …
linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection …
Solving linear systems on a GPU with hierarchically off-diagonal low-rank approximations
We are interested in solving linear systems arising from three applications:(1) kernel
methods in machine learning,(2) discretization of boundary integral equations from …
methods in machine learning,(2) discretization of boundary integral equations from …
[BOOK][B] Numerical linear algebra with Julia
E Darve, M Wootters - 2021 - SIAM
51. Gu, M. & Eisenstat, SC A divide-and-conquer algorithm for the bidiagonal SVD. SIAM
Journal on Matrix Analysis and Applications 16, 79–92 (1995)(cit. on p. 199). 52. Jones, MT …
Journal on Matrix Analysis and Applications 16, 79–92 (1995)(cit. on p. 199). 52. Jones, MT …
Performance portable ice-sheet modeling with MALI
High-resolution simulations of polar ice sheets play a crucial role in the ongoing effort to
develop more accurate and reliable Earth system models for probabilistic sea-level …
develop more accurate and reliable Earth system models for probabilistic sea-level …
Sparse hierarchical solvers with guaranteed convergence
Solving sparse linear systems from discretized partial differential equations is challenging.
Direct solvers have, in many cases, quadratic complexity (depending on geometry), while …
Direct solvers have, in many cases, quadratic complexity (depending on geometry), while …
[HTML][HTML] A fast direct solver for nonlocal operators in wavelet coordinates
In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to
combine a wavelet representation of the system matrix, yielding a quasi-sparse matrix, with …
combine a wavelet representation of the system matrix, yielding a quasi-sparse matrix, with …
Tuning the perplexity for and computing sampling-based t-SNE embeddings
Widely used pipelines for the analysis of high-dimensional data utilize two-dimensional
visualizations. These are created, eg, via t-distributed stochastic neighbor embedding (t …
visualizations. These are created, eg, via t-distributed stochastic neighbor embedding (t …
Sparse hierarchical preconditioners using piecewise smooth approximations of eigenvectors
B Klockiewicz, E Darve - SIAM Journal on Scientific Computing, 2020 - SIAM
When solving linear systems arising from PDE discretizations, iterative methods (such as
conjugate gradient (CG), GMRES, or MINRES) are often the only practical choice. To …
conjugate gradient (CG), GMRES, or MINRES) are often the only practical choice. To …
Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems
We describe a second‐order accurate approach to sparsifying the off‐diagonal matrix blocks
in the hierarchical approximate factorization methods for solving sparse linear systems …
in the hierarchical approximate factorization methods for solving sparse linear systems …
Hierarchical subspace evolution method for super large parallel computing: A linear solver and an eigensolver as examples
H Xu, B Liu - International Journal for Numerical Methods in …, 2023 - Wiley Online Library
Solving linear equations and finding eigenvalues are essential tasks in many simulations for
engineering applications, but these tasks often cause performance bottlenecks. In this work …
engineering applications, but these tasks often cause performance bottlenecks. In this work …