Balancing vectors in the max norm
Combinatorica
A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection
The Journal of Machine Learning Research
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Sampling from large matrices: An approach through geometric functional analysis
Journal of the ACM (JACM)
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Efficient algorithms using the multiplicative weights update method
Efficient algorithms using the multiplicative weights update method
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners
SIAM Journal on Numerical Analysis
Proceedings of the forty-first annual ACM symposium on Theory of computing
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
A note on element-wise matrix sparsification via a matrix-valued Bernstein inequality
Information Processing Letters
Random Cayley graphs and expanders
Random Structures & Algorithms
Spectral sparsification and restricted invertibility
Spectral sparsification and restricted invertibility
Low rank matrix-valued chernoff bounds and approximate matrix multiplication
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Moment inequalities for sums of random matrices and their applications in optimization
Mathematical Programming: Series A and B
A fast random sampling algorithm for sparsifying matrices
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
A Simpler Approach to Matrix Completion
The Journal of Machine Learning Research
Strong converse for identification via quantum channels
IEEE Transactions on Information Theory
User-Friendly Tail Bounds for Sums of Random Matrices
Foundations of Computational Mathematics
On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs
Combinatorics, Probability and Computing
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In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which the matrices have a group structure and an other in which they have rank-one. As an application of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, it constructs an expanding Cayley graph of logarithmic degree in near-optimal $\mathcal{O}(n^2\log^3 n)$ time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices, which implies an improved deterministic algorithm for spectral graph sparsification of dense graphs. In addition, we give an elementary connection between spectral sparsification of positive semi-definite matrices and element-wise matrix sparsification. As a consequence, we obtain improved element-wise sparsification algorithms for diagonally dominant-like matrices.