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Dynamic Matrix Inverse: Improved Algorithms and Matching Conditional Lower Bounds [article]

Jan van den Brand, Danupon Nanongkai, Thatchaphol Saranurak
2019 arXiv   pre-print
In this paper, we present (i) improved algorithms for dynamic matrix inverse and their extensions to some incremental/look-ahead variants, and (ii) variants of the Online Matrix-Vector conjecture [Henzinger  ...  The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates.  ...  Danupon Nanongkai and Thatchaphol Saranurak were also partially supported by the Swedish Research Council (Reg. No. 2015-04659).  ... 
arXiv:1905.05067v1 fatcat:2jtnqgchnndirmi7wcpcl2cpcm

Faster Dynamic Matrix Inverse for Faster LPs [article]

Shunhua Jiang, Zhao Song, Omri Weinstein, Hengjie Zhang
2020 arXiv   pre-print
Our techniques and amortized analysis of multi-level partial updates, may be of broader interest to dynamic matrix problems.  ...  Motivated by recent Linear Programming solvers, we design dynamic data structures for maintaining the inverse of an n× n real matrix under low-rank updates, with polynomially faster amortized running time  ...  [BNS19] Jan van den Brand, Danupon Nanongkai, and Thatchaphol Saranurak. Dynamic matrix inverse: Improved algorithms and matching conditional lower bounds.  ... 
arXiv:2004.07470v1 fatcat:rs2tcefa4jgd7hbycxhp3vrfxy

Dynamic Boolean Matrix Factorizations

Pauli Miettinen
2012 2012 IEEE 12th International Conference on Data Mining  
The results show that with good initialization the proposed online and dynamic methods can beat the stateof-the-art offline Boolean matrix factorization algorithms.  ...  This paper proposes a method to dynamically update the Boolean matrix factorization when new data is added to the data base.  ...  CONCLUSIONS We have presented algorithms for doing dynamic and online Boolean matrix factorizations.  ... 
doi:10.1109/icdm.2012.118 dblp:conf/icdm/Miettinen12 fatcat:iy7ibo62y5ch7j5h4moucwjoyy

A State-Space Approach to Dynamic Nonnegative Matrix Factorization

Nasser Mohammadiha, Paris Smaragdis, Ghazaleh Panahandeh, Simon Doclo
2015 IEEE Transactions on Signal Processing  
We use expectation maximization and propose a maximum-likelihood estimation framework to estimate the basis matrix and the N-VAR model parameters.  ...  Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade.  ...  The EM algorithm maximizes a lower bound on and iterates between an expectation (E) step and a maximization (M) step until convergence.  ... 
doi:10.1109/tsp.2014.2385655 fatcat:q4lkpa4z55btleuvhrt2pyjtwi

Collaborative Kalman Filtering for Dynamic Matrix Factorization

John Z. Sun, Dhruv Parthasarathy, Kush R. Varshney
2014 IEEE Transactions on Signal Processing  
Suited for use in collaborative filtering settings encountered in recommendation systems with significant temporal dynamics in user preferences, the approach extends probabilistic matrix factorization  ...  We propose a new algorithm for estimation, prediction, and recommendation named the collaborative Kalman filter.  ...  K Goyal and A. Mojsilović for support, and the anonymous reviewers for many helpful comments.  ... 
doi:10.1109/tsp.2014.2326618 fatcat:wtf3uchb3jba7ag6fpo7qlzrpq

Out-of-equilibrium dynamics with matrix product states

M L Wall, Lincoln D Carr
2012 New Journal of Physics  
Furthermore, by using the Matrix Product Operator (MPO) formalism, one can exactly represent the Hamiltonian and other operators.  ...  Our algorithms use only the MPO form of the Hamiltonian, and so are applicable to microscopic degrees of freedom of any variety, and do not require Hamiltonian-specialized implementation.  ...  The mixed canonical form is crucial for improving the speed and numerical stability of variational algorithms with MPSs.  ... 
doi:10.1088/1367-2630/14/12/125015 fatcat:2xejefhxkjgvfgnxo7kzt2ke34

Stable inverse dynamic curves

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Joëlle Thollot
2010 ACM Transactions on Graphics  
Then we show how to compute the physical parameters of a dynamic rod model (super-circle) so that its stable rest shape under gravity exactly matches the fitted circular arcs curve.  ...  We demonstrate the interactivity and controllability of our approach on various examples where a user can intuitively setup efficient and precise 2d animations by specifying the input geometry.  ...  Acknowledgments We would like to thank Laurence Boissieux for her artistic contribution to the paper, Basile Audoly for sharing with us the original code on 2d super-helices, and the anonymous reviewers  ... 
doi:10.1145/1882261.1866159 fatcat:d27ho6yqmfgypo7noygykd4a3m

Stable inverse dynamic curves

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Joëlle Thollot
2010 ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10  
Then we show how to compute the physical parameters of a dynamic rod model (super-circle) so that its stable rest shape under gravity exactly matches the fitted circular arcs curve.  ...  We demonstrate the interactivity and controllability of our approach on various examples where a user can intuitively setup efficient and precise 2d animations by specifying the input geometry.  ...  Acknowledgments We would like to thank Laurence Boissieux for her artistic contribution to the paper, Basile Audoly for sharing with us the original code on 2d super-helices, and the anonymous reviewers  ... 
doi:10.1145/1882262.1866159 fatcat:galcedwuqjen7goletonloy2pe

Stable inverse dynamic curves

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Joëlle Thollot
2010 ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10  
Then we show how to compute the physical parameters of a dynamic rod model (super-circle) so that its stable rest shape under gravity exactly matches the fitted circular arcs curve.  ...  We demonstrate the interactivity and controllability of our approach on various examples where a user can intuitively setup efficient and precise 2d animations by specifying the input geometry.  ...  Acknowledgments We would like to thank Laurence Boissieux for her artistic contribution to the paper, Basile Audoly for sharing with us the original code on 2d super-helices, and the anonymous reviewers  ... 
doi:10.1145/1866158.1866159 fatcat:ahh2d2ezy5betgodhoxuxgawq4

Dynamical correlation functions using the density matrix renormalization group

Till D. Kühner, Steven R. White
1999 Physical Review B (Condensed Matter)  
By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results.  ...  The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems.  ...  The band presented in Fig. 8 shows the correct upper and lower bound, but the spectral weight in the band decays faster than 1/ω.  ... 
doi:10.1103/physrevb.60.335 fatcat:xpjdgsaoxjdajbgmsg4iymyezq

Large N classical dynamics of holographic matrix models [article]

Curtis T. Asplund, David Berenstein, Eric Dzienkowski
2012 arXiv   pre-print
Using a numerical simulation of the classical dynamics of the plane-wave and flat space matrix models of M-theory, we study the thermalization, equilibrium thermodynamics and fluctuations of these models  ...  We show evidence for thermalization by matching the time-averaged distributions of the matrix eigenvalues to the distributions of the appropriate Traceless Gaussian Unitary Ensemble of random matrices.  ...  Srednicki, and E. Shuryak for various discussions related to this work. We thank J.  ... 
arXiv:1211.3425v1 fatcat:vvha2hz5djdu7g2rrxwmtor66q

Learning to Match via Inverse Optimal Transport [article]

Ruilin Li, Xiaojing Ye, Haomin Zhou, Hongyuan Zha
2018 arXiv   pre-print
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict  ...  Our model falls into the category of prescriptive models, which not only predict potential future matching, but is also able to explain what leads to empirical matching and quantifies the impact of changes  ...  Proposition 3 If empiricalμ,ν are off from true µ, ν by ∆µ, ∆ν, then the matching matrix π IOT recovered by solving equation (2) has error lower bounded by π 0 − π IOT 1 ≥ ∆µ 2 1 + ∆ν 2 1 mn where π  ... 
arXiv:1802.03644v3 fatcat:35t7drwsyfdr7jbgbpcit3og5m

Efficient DMFT impurity solver using real-time dynamics with matrix product states

Martin Ganahl, Markus Aichhorn, Hans Gerd Evertz, Patrik Thunström, Karsten Held, Frank Verstraete
2015 Physical Review B  
We apply the method as an impurity solver within the Dynamical Mean Field Theory (DMFT) for the single- and two-band Hubbard model on the Bethe lattice.  ...  The resolution of the spectral function is improved by a so-called linear prediction approach.  ...  Acknowledgments The authors acknowledge financial support by the Austrian Science Fund (FWF) through SFB ViCoM F41 projects P03 and P04 (FWF project ID F4103-N13 and F4104-N13) and NAWI Graz.  ... 
doi:10.1103/physrevb.92.155132 fatcat:y4zqd5egivf45gmvk7mvr4n7tq

Robust tuning of dynamic matrix controllers for first order plus dead time models

Peyman Bagheri, Ali Khaki Sedigh
2015 Applied Mathematical Modelling  
Dynamic Matrix Control is a widely used Model Predictive Controller in industrial processes.  ...  Finally, a tuning boundary is derived which gives the lower and upper permissible bounds for the tuning parameter that guarantee the robust performance of the uncertain first order plus dead time plant  ...  (LMI) solves the inverse problem of controller matching which numerically tunes the weight matrices.  ... 
doi:10.1016/j.apm.2015.02.035 fatcat:t62tm7gpnvfb3e43nzhungmr6q

Robust Inverse Reinforcement Learning under Transition Dynamics Mismatch [article]

Luca Viano, Yu-Ting Huang, Parameswaran Kamalaruban, Adrian Weller, Volkan Cevher
2021 arXiv   pre-print
We study the inverse reinforcement learning (IRL) problem under a transition dynamics mismatch between the expert and the learner.  ...  Finally, we empirically demonstrate the stable performance of our algorithm compared to the standard MCE IRL algorithm under transition dynamics mismatches in both finite and continuous MDP problems.  ...  Acknowledgments and Disclosure of Funding  ... 
arXiv:2007.01174v4 fatcat:44vxl2ec7bf2pk7o3oepvjhhae
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