
Efficient construction of an HSS preconditioner for symmetric positive definite ℋ^2 matrices
In an iterative approach for solving linear systems with illconditioned...
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Sumofsquares chordal decomposition of polynomial matrix inequalities
We prove three decomposition results for sparse positive (semi)definite...
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ACCAMS: Additive CoClustering to Approximate Matrices Succinctly
Matrix completion and approximation are popular tools to capture a user'...
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Practical Algorithms for Learning NearIsometric Linear Embeddings
We propose two practical nonconvex approaches for learning nearisometr...
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Parallelization and scalability analysis of inverse factorization using the Chunks and Tasks programming model
We present three methods for distributed memory parallel inverse factori...
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Genomescale estimation of cellular objectives
Cellular metabolism is predicted accurately at the genomescale using co...
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Matrix optimization on universal unitary photonic devices
Universal unitary photonic devices are capable of applying arbitrary uni...
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Optimal Approximation of Doubly Stochastic Matrices
We consider the leastsquares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the wellknown Alternating Direction Method of Multipliers (ADMM) to a reformulation of the original problem. Our resulting algorithm requires an initial Cholesky factorization of a positive definite matrix that has the same sparsity pattern as C + I followed by simple iterations whose complexity is linear in the number of nonzeros in C, thus ensuring excellent scalability and speed. We demonstrate the advantages of our approach in a series of experiments on problems with up to 82 million nonzeros; these include normalizing large scale matrices arising from the 3D structure of the human genome, clustering applications, and the SuiteSparse matrix library. Overall, our experiments illustrate the outstanding scalability of our algorithm; matrices with millions of nonzeros can be approximated in a few seconds on modest desktop computing hardware.
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