Ivan Oseledets homepage

2013 is now in its full rights, so it is time to go on with research.
With Chris­t­ian Lubich we have fin­ished a paper on a very effi­cient time-stepping scheme for the dynam­i­cal low-rank approx­i­ma­tion — so-called KLS-scheme, which is remark­ably sim­ple but effi­cient to com­pute the dynam­ics on low-rank man­i­folds. It presents a full analy­sis for the two-dimensional case, with mul­ti­di­men­sional case (TT-format) in progress.

One more old paper on explicit rep­re­sen­ta­tions of sim­ple func­tions in ten­sor for­mats is pub­lished in the Con­struc­tive Approximation!

Our paper on the new time-stepping scheme based on the QTT-format has been pub­lished in SISC!

Four papers are in progress : on the block eigen­value solver in the TT-format, on the dynam­i­cal low-rank approx­i­ma­tion, on the ten­sor struc­ture of the wavelet ten­sor train matrix and on the fast solu­tion of the Stokes prob­lem in ten­sor for­mat. Hope to fin­ish them soon.

Also, I put some time to get an imple­men­ta­tion of the TT-Toolbox in Python. The pre­lim­i­nary ver­sion (ttpy 0.1) is avail­able on the github. Please take a look on it, if you are interested.

We have recently put the pub­li­ca­tions of our research group at the Insti­tute of Numer­i­cal Math­e­mat­ics RAS on the web. The list is not yet full, but is close. Check it!

This paper with Dmitry Savostyanov pub­lished in the end of 2011 in the Pro­ceed­ings of 7th Inter­na­tional Work­shop on Mul­ti­di­men­sional Sys­tems (nDS), doi: 10.1109/nDS.2011.6076873 is about fast adap­tive meth­ods for the approx­i­ma­tion of high-dimensional arrays by cross-type meth­ods (such meth­ods are quite pop­u­lar for matrices).

We did it in our recent paper Effi­cient time-stepping scheme for dynam­ics on TT-manifolds , which is pub­lished as a preprint in MIS MPI Leipzig. In fact, we man­aged to pro­vide an effi­cient numer­i­cal scheme for the com­pu­ta­tion of the TT-dynamics. The MATLAB imple­men­ta­tion will be soon included in the devel­op­ment github repos­i­tory of the TT-Toolbox.

TT-Toolbox (TT=Tensor Train) Ver­sion 2.2

TT(Tensor Train) for­mat is an effi­cient way for low-parametric
rep­re­sen­ta­tion of high-dimensional ten­sors. The TT-Toolbox
is a MATLAB imple­men­ta­tion of basic oper­a­tions with
ten­sors in TT-format. It includes:

* tt_tensor and tt_matrix classes for stor­ing vec­tors and oper­a­tors
* Basic lin­ear alge­bra sub­rou­tines (addi­tion, matrix-by-vector prod­uct,
ele­men­t­wise mul­ti­pli­ca­tion and many oth­ers) using stan­dard MATLAB syn­tax,
lin­ear com­plex­ity in the dimen­sion, reshape func­tion
* Fast round­ing pro­ce­dure with a pre­scribed accu­racy
* Advanced approx­i­ma­tion and solu­tion techniques:

* Approx­i­mate solu­tion of lin­ear sys­tems and eigen­value prob­lems
* Cross meth­ods to approx­i­mate “black-box” ten­sors
* Wavelet ten­sor train decomposition

* Con­struc­tion of basic oper­a­tors and func­tions (Laplace oper­a­tor, func­tion of a TT-tensor)
* Com­pu­ta­tion of max­i­mal and min­i­mal ele­ments of a ten­sor
* and sev­eral others

New in Ver­sion 2.2

* Bet­ter doc­u­men­ta­tion
* Mixed QTT-Tucker for­mat (qtt_tucker class)
* reshape func­tion for a TT-tensor/TT-matrix
* dmrg_cross method for black-box ten­sor approx­i­ma­tion
* Con­vo­lu­tion in QTT-format

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Google myc­i­ta­tions ser­vice looks great. Here is mine

I decided to by on a twit­ter also (now posts only in Russ­ian, but who knows )

oseledet­si­van