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Limits on the Universal Method for Matrix Multiplication [article]

Josh Alman
2019 arXiv   pre-print
In this work, we prove limitations on the known methods for designing matrix multiplication algorithms.  ...  Our main result is that the Universal method applied to any Coppersmith-Winograd tensor CW_q cannot yield a bound on ω, the exponent of matrix multiplication, better than 2.16805.  ...  Acknowledgements I would like to thank Matthias Christandl, Joshua Grochow, Ryan Williams, Virginia Vassilevska Williams, and Jeroen Zuiddam for helpful discussions and suggestions.  ... 
arXiv:1812.08731v2 fatcat:wsb65p3vcrfmnld3qjpzo4mava

Limits on the Universal Method for Matrix Multiplication

Josh Alman, Michael Wagner
2019 Computational Complexity Conference  
In this work, we prove limitations on the known methods for designing matrix multiplication algorithms.  ...  Our main result is that the Universal method applied to any Coppersmith-Winograd tensor CWq cannot yield a bound on ω, the exponent of matrix multiplication, better than 2.16805.  ...  Limits on the Universal Method for Matrix Multiplication The Galactic Method lower bounds of [2] were proved by introducing a suite of tools for giving upper bounds on Ĩ(T ), the asymptotic independence  ... 
doi:10.4230/lipics.ccc.2019.12 dblp:conf/coco/Alman19 fatcat:wtwidmi555cmfmisje2oe4ldyq

Page 752 of The Journal of the Operational Research Society Vol. 53, Issue 7 [page]

2002 The Journal of the Operational Research Society  
The steady state probability vector can be solved by using one of the following five methods: 1. truncation of the state space, 2. the matrix geometric method for matrices of the G/M/1 type,” methods for  ...  or methods based on obtaining the eigenvalue and eigen- vectors of difference equations involving the steady state probabilities. '” In this paper we use the matrix geometric method to obtain the joint  ... 

Page 703 of Behavior Research Methods Vol. 13, Issue 5 [page]

1981 Behavior Research Methods  
The only machine-specific limitations may be in the use of multiple statements on a line and APPLESOFT’S use of character strings in “input” statements.  ...  While this method is effective for small problems and allows the use of an unlimited number of subjects, the method is too slow for entering large data sets.  ... 

What is the value of limited feedback for MIMO channels?

D.J. Love, R.W. Heath, W. Santipach, M.L. Honig
2004 IEEE Communications Magazine  
and support for multiple users.  ...  Subspace distances can be defined in a number of different ways and are dependent on the dimension M chosen for the precoder matrix.  ... 
doi:10.1109/mcom.2004.1341261 fatcat:hz4yszo3vngb7k6ojqm35flr5y

Mufact: An Algorithm for Multiple Factor Analyses of Singular and Nonsingular Data With Orthogonal and Oblique Transformation Solutions

Richard J. Hofmann
1978 Educational and Psychological Measurement  
Multiple factor analysis. Chicago: University of Chi- cago Press, 1947. — L. L. The vectors of mind. Chicago: University of Chicago,  ...  The computer algorithm is highly transportable with minimum limi- tations on number of variables and no limitations on the number of observations.  ... 
doi:10.1177/001316447803800119 fatcat:drkfkkevd5a4xktnooks3jcbmy

Page 97 of Behavioral Science Vol. 6, Issue 1 [page]

1961 Behavioral Science  
Princeton: Princeton University Press, 1956. Pp. 235- 252. Miller, G. A. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol.  ...  Limitations: The factor matrix may not exceed 40 variables or 10 factors, the correlation matrix may not  ... 

Algorithmic Complexities in Backpropagation and Tropical Neural Networks [article]

Ozgur Ceyhan
2021 arXiv   pre-print
the complexity of usual multiplication.  ...  We then explore artificial neural networks in terms of tropical arithmetics and tropical algebraic geometry, and introduce the multi-layered tropical neural networks as universal approximators.  ...  Acknowledgments I wish to thank to Grisha Mikhalkin, not only for introducing me to the tropical geometry over the years, but also for inviting me over to Geneva (in various occasions) and listening my  ... 
arXiv:2101.00717v1 fatcat:lhovywrgizbbrhps4xe4ujkuva

Some formulas for estimating tracking errors

Walter R. Innes
1993 Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment  
Universal curves and approximate formulas for the elements of the track parameter error matrix are derived for homogeneous tracking detectors in the continuous measurement limit.  ...  Figures 1 through 6 show the universal curves for all the matrix elements .  ...  Let's assume for the moment that in this limit there is universal curve, i.e., that the . . same curve (up to scale factors in length and magnitude) which describes a matrix element's dependence on length  ... 
doi:10.1016/0168-9002(93)90942-b fatcat:2pdf7wsrlzcwdnu5wrvh2digje

The Euclid Statistical Matrix Tool

Curtis Tilves, Saeed Yekaninejad, Tetsuro Hayashi, Eman Eltahlawy, Eugene Shubnikov, Shalkar Adambekov
2017 Central Asian Journal of Global Health  
ways of learning materials, and language barriers.We present here the Euclid Statistical Matrix, a tool for combatting Stataphobia on a global scale.  ...  Future dissemination of the Euclid Statistical Matrix throughout the Central Asia and support from local universities may help to combat low research productivity in this region.  ...  Acknowledgments We would like to thank the Library of Alexandria, Egypt, for their wonderful support and services.  ... 
doi:10.5195/cajgh.2017.283 pmid:29138739 pmcid:PMC5675393 fatcat:az4ysj7f4fhfpnhh2jf65mpyr4

New Strategies for Associative Memories
English

2018 Engineering and Technology Journal  
A modified strategy is suggested to overcome these limitations by introducing a new algorithm to the design of the associative memory. This method provides a software solution to the problems.  ...  There are two matters which limit the uses of associative memory; the limited storage capacity, and the error occurred in the reading of output data.  ...  pairs without any limitations on its storage capacity.  ... 
doi:10.30684/etj.36.2a.13 fatcat:lqc4opoxxzgpni6yirront7vf4

The April Meeting of the Kentucky Section

V. F. Cowling
1958 The American mathematical monthly  
Multiplication on the real line, by Professor J. G. Horne, University of Kentucky.  ...  =#, the resulting equation is a first order linear differential equation. This is then solved by the usual methods. 8. A network of checks for the multiplication of matrices, by Professor J. C.  ... 
doi:10.1080/00029890.1958.11991964 fatcat:qphx3cevqrhtbosyrqf3ffvodu

Development of efficient computational kernels and linear algebra routines for out-of-order superscalar processors

O. Bessonov, D. Fougère, B. Roux
2005 Future generations computer systems  
Approaches for implementing matrix multiplication algorithms are suggested for hierarchical memory computers. Block versions of matrix multiplication and LUdecomposition algorithms are considered.  ...  We present methods for developing high performance computational kernels and dense linear algebra routines.  ...  Acknowledgements This work was partially supported by the Russian Foundation for Basic Research (grants 01-01-00745 and 02-01-00210).  ... 
doi:10.1016/j.future.2004.05.016 fatcat:rtfuljawdvh3pkow5a4xl5xnn4

Joint sparse representation based classification of rub-impact in rotating machinery with multiple acoustic emission sensors

Liping Shi, Wei Peng, Jing Li, Weidong Liu, Han Li
2018 Journal of Vibroengineering  
This paper investigates the use of multiple AE sensors for the classification of rub-impact in rotating machinery based on the JSRC method.  ...  Then, the extracted cepstral features of all AE sensors are concatenated as the input matrix for the JSRC based classifier.  ...  For the JSRC method, the matrix defined in Eq. (16) is constraint to be row wise sparse.  ... 
doi:10.21595/jve.2017.18292 fatcat:nke5z7tzvnfurcsx72jlgii2be

BASIC BACKSTEP: A simple backward-selection multiple-regression program for minicomputers and microcomputers

Bernard S. Gorman, Louis H. Primavera
1981 Behavior Research Methods  
The only machine-specific limitations may be in the use of multiple statements on a line and APPLESOFT's use of character strings in "input" statements.  ...  While this method is effective for small problems and allows the use of an unlimited number of subjects, the method is too slow for entering large data sets.  ... 
doi:10.3758/bf03202101 fatcat:z6zo2mhcbzh3jfst3kmawv44ue
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