Hybrid H_h-matrices with adaptive mixed precision achieve up to 11x storage savings versus standard double-precision H-matrices while preserving accuracy in matrix-vector products.
Bebendorf, Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, Springer
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Introduces efficient H²_* (fully nested) and (H² + H)_* (semi-nested) algebraic algorithms based on weak admissibility for fast MVP in 2D/3D N-body problems, shown competitive with standard H² methods in tests.
Adaptive matrix-free randomized QB algorithms determine rank on the fly via sketched residual indicators and pruning, meeting Frobenius or spectral tolerances to machine precision with near-optimal ranks.
citing papers explorer
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Hybrid hierarchical matrices with adaptive mixed precision storage
Hybrid H_h-matrices with adaptive mixed precision achieve up to 11x storage savings versus standard double-precision H-matrices while preserving accuracy in matrix-vector products.
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New Algebraic Fast Algorithms for $N$-body Problems in Two and Three Dimensions
Introduces efficient H²_* (fully nested) and (H² + H)_* (semi-nested) algebraic algorithms based on weak admissibility for fast MVP in 2D/3D N-body problems, shown competitive with standard H² methods in tests.
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Adaptive, Matrix-Free Low-Rank Approximation
Adaptive matrix-free randomized QB algorithms determine rank on the fly via sketched residual indicators and pruning, meeting Frobenius or spectral tolerances to machine precision with near-optimal ranks.