Dr Dmitry Savostyanov
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Email
d.savostyanov@essex.ac.uk -
Telephone
+44 (0) 1206 876065
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Location
2.528, Colchester Campus
Profile
Biography
I develop efficient algorithms for high-dimensional problems using low-rank tensor product approximations, linear and multilinear algebra, matrix analysis, and other methods of modern numerical mathematics.
Qualifications
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PhD (Cand. Sci.) in Computational Mathematics Institute of Numerical Mathematics of Russian Academy of Sciences, (2006)
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MSc in Applied Physics and Mathematics Moscow Institute of Physics and Technology, (2003)
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BSc in Applied Physics and Mathematics Institute of Physics and Technology, (2001)
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PGCert in Learning and Teaching in Higher Education University of Brighton, (2016)
Appointments
Other academic
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Senior Lecturer, Computing, Engineering and Mathematics, University of Brighton (20/10/2014 - 31/1/2020)
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Senior Research Fellow, Chemistry, University of Southampton (1/10/2012 - 30/9/2014)
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Leverhulme Trust Visiting Research Fellow, Mathematical and Physical Sciences, University of Chester (1/10/2011 - 30/9/2012)
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Researcher, Institute of Numerical Mathematics of Russian Academy of Sciences (1/1/2007 - 30/9/2011)
Research and professional activities
Research interests
High-dimensional problems
High-dimensional problems appear in a variety of applications, including quantum physics and chemistry, probability and statistics, stochastic differential equations, problems with uncertain parameters or noise. Typically, these problems are too complex to be solved using pen and paper only --- numerical methods and high-performance calculations are essential. However, the numerical complexity (computer memory and time required to crunch the numbers) grow exponentially with the dimension and standard off-the-shelf algorithms struggle. To break the curse of dimensionality, we need to develop a new family of effective algorithms, capable to meet the main computational challenge of the 21st century.
Tensor product decompositions
To break the curse of dimensionality and make high-dimensional problems possible to solve in our computational practice, we need to develop a new family of effective algorithms. One of the most promising approaches is based on the idea of tensor product decomposition. Similar to a low-rank decomposition of a matrix, tensor product decomposition applied to a high-dimensional array (tensor) or a multivariate function separates the variables (indices) and treats each dimension (mode) separately. In many applications this leads to exponential savings of computational costs, dramatically reducing the time required to solve the problem and improving the accuracy of the results. Often the problems which were considered impossible to solve become possible with the help of tensor product decompositions.
Teaching and supervision
Current teaching responsibilities
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Mathematical and Computational Modelling (MA185)
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Numerical Methods (MA209)
Current supervision
Publications
Publications (1)
Dolgov, S. and Savostyanov, D., (2024). Tensor product algorithms for inference of contact network from epidemiological data
Journal articles (27)
Dolgov, S. and Savostyanov, D., (2024). Tensor product approach to modelling epidemics on networks. Applied Mathematics and Computation. 460, 128290-128290
Chatzigeorgiou, I. and Savostyanov, D., (2024). Guessing Random Additive Noise Decoding of Network Coded Data Transmitted over Burst Error Channels. IEEE Transactions on Vehicular Technology, 1-16
Dolgov, S. and Savostyanov, D., (2020). Parallel cross interpolation for high-precision calculation of high-dimensional integrals. Computer Physics Communications. 246, 106869-106869
Dolgov, S., Pearson, JW., Savostyanov, DV. and Stoll, M., (2016). Fast tensor product solvers for optimization problems with fractional differential equations as constraints. Applied Mathematics and Computation. 273, 604-623
Dolgov, SV. and Savostyanov, DV., (2015). Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. Lecture Notes in Computational Science and Engineering. 103, 335-343
Edwards, LJ., Savostyanov, DV., Welderufael, ZT., Lee, D. and Kuprov, I., (2014). Quantum mechanical NMR simulation algorithm for protein-size spin systems. Journal of Magnetic Resonance. 243, 107-113
Dolgov, SV., Khoromskij, BN., Oseledets, IV. and Savostyanov, DV., (2014). Computation of extreme eigenvalues in higher dimensions using block tensor train format. Computer Physics Communications. 185 (4), 1207-1216
Roberts, JA., Savostyanov, DV. and Tyrtyshnikov, EE., (2014). Superfast solution of linear convolutional Volterra equations using QTT approximation. Journal of Computational and Applied Mathematics. 260, 434-448
Ford, NJ., Savostyanov, DV. and Zamarashkin, NL., (2014). On the Decay of the Elements of Inverse Triangular Toeplitz Matrices. SIAM Journal on Matrix Analysis and Applications. 35 (4), 1288-1302
Savostyanov, DV., (2014). Quasioptimality of maximum-volume cross interpolation of tensors. Linear Algebra and Its Applications. 458, 217-244
Savostyanov, DV., Dolgov, SV., Werner, JM. and Kuprov, I., (2014). Exact NMR simulation of protein-size spin systems using tensor train formalism. Physical Review B. 90 (8), 085139-
Dolgov, SV. and Savostyanov, DV., (2014). Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions. SIAM Journal on Scientific Computing. 36 (5), A2248-A2271
Edwards, LJ., Savostyanov, DV., Nevzorov, AA., Concistrè, M., Pileio, G. and Kuprov, I., (2013). Grid-free powder averages: On the applications of the Fokker–Planck equation to solid state NMR. Journal of Magnetic Resonance. 235, 121-129
Goreinov, SA., Oseledets, IV. and Savostyanov, DV., (2012). Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case. SIAM Journal on Scientific Computing. 34 (1), A1-A27
Savostyanov, DV., Tyrtyshnikov, EE. and Zamarashkin, NL., (2012). Fast truncation of mode ranks for bilinear tensor operations. Numerical Linear Algebra with Applications. 19 (1), 103-111
Savostyanov, D., (2012). QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images. Linear Algebra and its Applications. 436 (9), 3215-3224
Dolgov, S., Khoromskij, B. and Savostyanov, D., (2012). Superfast Fourier Transform Using QTT Approximation. Journal of Fourier Analysis and Applications. 18 (5), 915-953
Oseledets, IV., Savostyanov, DV. and Tyrtyshnikov, EE., (2010). Cross approximation in tensor electron density computations. Numerical Linear Algebra with Applications. 17 (6), 935-952
Savostyanov, DV., (2010). Tensor algorithms of blind separation of electromagnetic signals. Russian Journal of Numerical Analysis and Mathematical Modelling. 25 (4), 375-393
Savostyanov, DV. and Tyrtyshnikov, EE., (2009). Approximate multiplication of tensor matrices based on the individual filtering of factors. Computational Mathematics and Mathematical Physics. 49 (10), 1662-1677
Oseledets, IV., Savostyanov, DV. and Tyrtyshnikov, EE., (2009). Fast Simultaneous Orthogonal Reduction to Triangular Matrices. SIAM Journal on Matrix Analysis and Applications. 31 (2), 316-330
Savostyanov, DV., (2009). Fast Revealing of Mode Ranks of Tensor in Canonical Form. Numerical Mathematics: Theory, Methods and Applications. 2 (4), 439-444
Oseledets, IV., Savostyanov, DV. and Tyrtyshnikov, EE., (2009). Linear algebra for tensor problems. Computing. 85 (3), 169-188
Oseledets, IV., Savostianov, DV. and Tyrtyshnikov, EE., (2008). Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time. SIAM Journal on Matrix Analysis and Applications. 30 (3), 939-956
Flad, H-J., Khoromskij, BN., Savostyanov, DV. and Tyrtyshnikov, EE., (2008). Verification of the cross 3D algorithm on quantum chemistry data. Russian Journal of Numerical Analysis and Mathematical Modelling. 23 (4), 329-344
Oseledets, IV. and Savost’yanov, DV., (2006). Minimization methods for approximating tensors and their comparison. Computational Mathematics and Mathematical Physics. 46 (10), 1641-1650
Savost'yanov, DV. and Tyrtyshnikov, EE., (2004). On a case of the algebraic equivalence between the collocation and the Galerkin methods. Computational Mathematics and Mathematical Physics. 44 (4), 649-656
Book chapters (4)
Quiñones-Valles, D., Dolgov, S. and Savostyanov, D., (2019). Tensor Product Approach to Quantum Control. In: Integral Methods in Science and Engineering. Springer International Publishing. 367- 379. 9783030160760
Quiñones-Valles, D., Dolgov, S. and Savostyanov, D., (2019). Tensor Product Approach to Quantum Control. In: Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations. 367- 379. 9783030160760
Dolgov, SV. and Savostyanov, DV., (2015). Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm. In: Lecture Notes in Computational Science and Engineering. Springer International Publishing. 335- 343. 9783319107042
Goreinov, SA., Oseledets, IV., Savostyanov, DV., Tyrtyshnikov, EE. and Zamarashkin, NL., (2010). How to Find a Good Submatrix. In: Matrix Methods: Theory, Algorithms and Applications. WORLD SCIENTIFIC. 247- 256. 9812836012. 9789812836014
Conferences (2)
Savostyanov, D. and Oseledets, I., (2011). Fast adaptive interpolation of multi-dimensional arrays in tensor train format
Goreinov, SA., Savostyanov, DV., Tyrtyshnikov, EE. and ACAD, E., (2009). Tensor and Toeplitz Structures Applied to Direct and Inverse 3D Electromagnetic Problems
Other (2)
Dolgov, SV. and Savostyanov, DV., (2013).One-site density matrix renormalization group and alternating minimum energy algorithm. in Lecture Notes in Computational Science and Engineering.. 103
Dolgov, SV. and Savostyanov, DV., (2013).Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems. SIAM J. Sci. Comput. 36(5): A2248-A2271, 2014
Grants and funding
2021
Tensor product approach to black-box optimisation
Leverhulme Trust
