Randomized algorithms for matrix computations and analysis of high dimensional dataMartinsson, Gunnar
For commutingHermitianmatrices, there is a unitary matrixUthat jointly diagonalizes all matrices. For this significantly simpler situation, compared to the general non-Hermitian case, randomized methods based on (2) have recently been analyzed in [18], establishing favorable robustness and stability pr...
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over the Chebyshev a
First and second-order diffusive methods for rapid, coarse, distributed load balancing Theory Comput. Syst., 31 (1998), pp. 331-354 View in ScopusGoogle Scholar [24] Y. Rabani, A. Sinclair, R. Wanka Local divergence of Markov chains and the analysis of iterative load balancing schemes 39t...
Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the present work we examine generalizations of randomized matrix decomposition methods to higher order tensors in the framework of the hierarchical tensors representation. In particular we present...
Because of well-known reductions, our methods also yield equally ecient algorithms for fundamental problems like the convex hull in three dimensions, Voronoi diagram of point sites on a plane and Euclidean minimal spanning tree. Our algorithms run in time T = O(log n) for worst-case inputs ...
Hence, the contribution of the paper is also in introducing proof methods whose further development could help the original problem in the general setting. Preliminary version of this paper was published as [11]. Results presented here are part of [12] as well. 1.1. Organization of the paper...
This randomized controlled study was designed to evaluate the effectiveness of computer-based cognitive training for improving cognitive function in such patients. Methods COG-T CHD is a multicenter, double-blind, parallel-designed, randomized controlled trial. The patients will be divided 1:1 into ...
Dunbar, O.R., Duncan, A.B., Stuart, A.M., Wolfram, M.-T.: Ensemble inference methods for models with noisy and expensive likelihoods. SIAM J. Appl. Dyn. Syst. 21(2), 1539–1572 (2022) MathSciNet Google Scholar Dunbar, O.R.A., Garbuno-Inigo, A., Schneider, T., Stuart,...
When the coefficient matrix is non-square, the row processing methods can be used to solve it. The Kaczmarz method is one of the classical row processing methods. In fact, the Kaczmarz method is a simple iteration projection method for solving large sparse linear systems [17]. It has been ...