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Mat. Zametki, 1997, Volume 62, Issue 4, Pages 619–623 (Mi mz1644)  

This article is cited in 29 scientific papers (total in 29 papers)

Brief Communications

Pseudo-skeleton approximations by matrices of maximal volume

S. A. Goreinov, N. L. Zamarashkin, E. E. Tyrtyshnikov

Institute of Numerical Mathematics, Russian Academy of Sciences


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English version:
Mathematical Notes, 1997, 62:4, 515–519

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Received: 29.04.1997
Revised: 10.06.1997

Citation: S. A. Goreinov, N. L. Zamarashkin, E. E. Tyrtyshnikov, “Pseudo-skeleton approximations by matrices of maximal volume”, Mat. Zametki, 62:4 (1997), 619–623; Math. Notes, 62:4 (1997), 515–519

Citation in format AMSBIB
\by S.~A.~Goreinov, N.~L.~Zamarashkin, E.~E.~Tyrtyshnikov
\paper Pseudo-skeleton approximations by matrices of maximal volume
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 4
\pages 619--623
\jour Math. Notes
\yr 1997
\vol 62
\issue 4
\pages 515--519

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    2. Engquist, B, “Fast directional multilevel algorithms for oscillatory kernels”, SIAM Journal on Scientific Computing, 29:4 (2007), 1710  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Rokhlin, V, “A RANDOMIZED ALGORITHM FOR PRINCIPAL COMPONENT ANALYSIS”, SIAM Journal on Matrix Analysis and Applications, 31:3 (2009), 1100  crossref  mathscinet  isi  scopus  scopus
    4. Caiafa C.F., Cichocki A., “Methods for Factorization and Approximation of Tensors by Partial Fiber Sampling”, 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (Camsap), IEEE, 2009, 73–76  crossref  isi  scopus  scopus
    5. Frederix K., Van Barel M., “Solving a Large Dense Linear System by Adaptive Cross Approximation”, J. Comput. Appl. Math., 234:11, SI (2010), 3181–3195  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Caiafa C.F., Cichocki A., “Generalizing the Column-Row Matrix Decomposition to Multi-Way Arrays”, Linear Alg. Appl., 433:3 (2010), 557–573  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Deshpande A., Rademacher L., “Efficient Volume Sampling for Row/Column Subset Selection”, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Soc, 2010, 329–338  crossref  mathscinet  isi  scopus  scopus
    8. Zhu X., Lin W., “Randomised Pseudo-Skeleton Approximation and its Application in Electromagnetics”, Electron. Lett., 47:10 (2011), 590–592  crossref  isi  elib  scopus  scopus
    9. Martinsson P.-G., Rokhlin V., Tygert M., “A Randomized Algorithm for the Decomposition of Matrices”, Appl. Comput. Harmon. Anal., 30:1 (2011), 47–68  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Civril A., Magdon-Ismail M., “Exponential Inapproximability of Selecting a Maximum Volume Sub-Matrix”, Algorithmica, 65:1 (2013), 159–176  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Boerm S., Goerdes J., “Low-Rank Approximation of Integral Operators by Using the Green Formula and Quadrature”, Numer. Algorithms, 64:3 (2013), 567–592  crossref  mathscinet  zmath  isi  scopus  scopus
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    13. Vervliet N., Debals O., Sorber L., De lathauwer L., “Breaking the Curse of Dimensionality Using Decompositions of Incomplete Tensors”, IEEE Signal Process. Mag., 31:5 (2014), 71–79  crossref  adsnasa  isi  scopus  scopus
    14. Savostyanov D.V., “Quasioptimality of Maximum-Volume Cross Interpolation of Tensors”, Linear Alg. Appl., 458 (2014), 217–244  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Civril A., “Column Subset Selection Problem Is Ug-Hard”, J. Comput. Syst. Sci., 80:4 (2014), 849–859  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Cichocki A., Mandic D.P., Anh Huy Phan, Caiafa C.F., Zhou G., Zhao Q., De Lathauwer L., “Tensor Decompositions For Signal Processing Applications”, IEEE Signal Process. Mag., 32:2 (2015), 145–163  crossref  adsnasa  isi  scopus  scopus
    17. Biagioni D.J., Beylkin D., Beylkin G., “Randomized Interpolative Decomposition of Separated Representations”, J. Comput. Phys., 281 (2015), 116–134  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    18. Litsarev M.S., Oseledets I.V., “Fast Low-Rank Approximations of Multidimensional Integrals in Ion-Atomic Collisions Modelling”, Numer. Linear Algebr. Appl., 22:6, SI (2015), 1147–1160  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Grasedyck L., Kriemann R., Loebbert Ch., Naegel A., Wittum G., Xylouris K., “Parallel Tensor Sampling in the Hierarchical Tucker Format”, Comput. Vis. Sci., 17:2 (2015), 67–78  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    21. Litsarev M.S., Oseledets I.V., “a Low-Rank Approach To the Computation of Path Integrals”, J. Comput. Phys., 305 (2016), 557–574  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    23. Cichocki A., Lee N., Oseledets I., Anh-Huy Phan, Zhao Q., Mandic D.P., “Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions”, Found. Trends Mach. Learn., 9:4-5 (2016), I+  crossref  isi  scopus
    24. Bigoni D., Engsig-Karup A.P., Marzouk Y.M., “Spectral Tensor-Train Decomposition”, SIAM J. Sci. Comput., 38:4 (2016), A2405–A2439  crossref  mathscinet  zmath  isi  elib  scopus
    25. Georgieva I. Hofreither C., “An algorithm for low-rank approximation of bivariate functions using splines”, J. Comput. Appl. Math., 310 (2017), 80–91  crossref  mathscinet  zmath  isi  elib  scopus
    26. Kumar N.K., Schneider J., “Literature Survey on Low Rank Approximation of Matrices”, Linear Multilinear Algebra, 65:11 (2017), 2212–2244  crossref  mathscinet  zmath  isi  scopus  scopus
    27. Boutsidis Ch., Woodruff D.P., “Optimal Cur Matrix Decompositions”, SIAM J. Comput., 46:2 (2017), 543–589  crossref  mathscinet  zmath  isi  scopus  scopus
    28. Litzinger F., Boninsegna L., Wu H., Nuske F., Patel R., Baraniuk R., Noe F., Clementi C., “Rapid Calculation of Molecular Kinetics Using Compressed Sensing”, J. Chem. Theory Comput., 14:5 (2018), 2771–2783  crossref  isi  scopus  scopus
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