MathDB4 problems
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Conjecture on removing the logarithmic factor in Cholesky estimation
Let denote the spatial resolution parameter in the estimator, and consider the upper bound in Theorem 2.2 for estimating the block Cholesky factor, which contains an a…
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The MF stack data-movement conjecture for sparse Cholesky methods
The sparse Cholesky methods MF, LL, and RL are compared through their factorization performance on large matrices. Method MF uses a stack whose data movement is described in line18…
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The serial assembly conjecture for sparse Cholesky methods
The methods LL, RL, and MF are compared on large sparse matrices using serial and multithreaded BLAS. Their assembly operations are performed serially, whereas RLB performs every f…
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Weak dependence of approximate Cholesky error on input sparsity
Weak-sparsity-dependence conjecture. The error of the approximate Cholesky factorization depends weakly on the number of non-zeros in the input Laplacian matrix.