2014
Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
Spielman D, Teng S. Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems. SIAM Journal On Matrix Analysis And Applications 2014, 35: 835-885. DOI: 10.1137/090771430.Peer-Reviewed Original ResearchDiagonal entriesInverse power methodLinear system solverDominant linear systemsLower asymptotic complexityLinear systemsLinear time algorithmNonzero structureCondition numberSystem solverDominant matricesFiedler vectorNonzero entriesPreconditionerAsymptotic complexityDevelopment of algorithmsRandomized algorithmSpecial casePower methodIntroduction of algorithmsRecursive fashionTime algorithmAlgorithmMatrixSolver
2013
Spectral sparsification of graphs
Batson J, Spielman D, Srivastava N, Teng S. Spectral sparsification of graphs. Communications Of The ACM 2013, 56: 87-94. DOI: 10.1145/2492007.2492029.Peer-Reviewed Original ResearchSpectral sparsificationApproximate maximum flowLinear systemsSpectral approximationLinear time algorithmCombinatorial optimizationGraph sparsificationLinear equationsDominant matricesArbitrary graphsSparse graphsFast solutionUndirected networksFast algorithmDevelopment of algorithmsSparsificationMinimum cutMaximum flowGraphApproximationAlgorithmEquationsOptimizationImportant toolSolution