Lecture 08: Partial Eigen Decomposition of Large Symmetric Matrices via Thick-Restart Lanczos with Explicit External Deflation and its Communication-Avoiding Variant
eigenpairs, symmetric matrix, explicit external deflation, backward stability, matrix powers kernal, algorithm
There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number of other advantages.
Bai, Z. (2021). Lecture 08: Partial Eigen Decomposition of Large Symmetric Matrices via Thick-Restart Lanczos with Explicit External Deflation and its Communication-Avoiding Variant. Mathematical Sciences Spring Lecture Series. Retrieved from https://scholarworks.uark.edu/mascsls/14
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