Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity (Q92247)
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scientific article; zbMATH DE number 7356307
- Compression, Inversion, and Approximate PCA of Dense Kernel Matrices at Near-Linear Computational Complexity
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity |
scientific article; zbMATH DE number 7356307 |
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7 June 2017
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8 June 2021
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math.NA
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cs.CC
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cs.DS
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cs.NA
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math.PR
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Compression, Inversion, and Approximate PCA of Dense Kernel Matrices at Near-Linear Computational Complexity (English)
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Cholesky factorization
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covariance function
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gamblet transform
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kernel matrix
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sparsity
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principal component analysis
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This article provides an overview of numerical methods for approximating and solving problems related to Gaussian processes, kernel matrices, and elliptic PDEs. It discusses various approaches for efficiency and accuracy, including sparse linear solvers (e.g., \multigrid, sparse Cholesky factorization) and low-rank approximations (Nyström, rank-revealing Cholesky factorization). Hierarchical methods (hierarchical matrices, HODLR, HSS matrices) and wavelet-based techniques are also highlighted. A notable contribution mentioned involves a modified Cholesky factorization for kernel matrices from elliptic PDE Green's functions, aiming for scalability and accuracy. Overall, the article showcases a range of solutions for computational challenges in these domains. (English)
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Scientists use various methods to solve complex math problems related to Gaussian processes and partial differential equations (PDEs). These problems often involve large amounts of data, making them hard to compute. To tackle this, researchers employ techniques like sparse linear solvers, low-rank approximations, hierarchical methods, and wavelet-based approaches. A new method, modifying an existing math tool called Cholesky factorization, shows promise in solving certain PDEs efficiently without needing overly complex structures. This variety of approaches helps scientists find the best way to solve their specific computational challenges. (English)
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0.7384325861930847
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