Pith. sign in

REVIEW 4 major objections 5 minor 38 references

TT-LSQR For Tensor Least Squares Problems and Application to Data Mining *

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A tensor-train reformulation of LSQR solves multiterm tensor least-squares problems without forming Kronecker products, and the paper shows the resulting solver classifies documents and images competitively.

desk verdict A plausible TT-LSQR extension whose truncation step is never shown to track the original least squares problem; worth refereeing, but the reliability claims need support. read the letter →

arxiv 2502.01293 v1 pith:7PIQVCC6 submitted 2025-02-03 math.NA cs.NA

Lorenzo Piccinini , Valeria Simoncini This is my paper · ORCID
classification math.NAcs.NA MSC 65F4565F5515A23
keywords tensorleastsquarestensor-trainformatLSQRranktruncationKroneckerproductsrandomizedsketchingdocumentclassificationimage
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the multiterm tensor least-squares problem $\min_{\mathcal{X}} \|\mathcal{F} - \sum_{i=1}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \cdots \times_d A_d^{(i)}\|_F$ can be solved by a tensor-train implementation of the classic iterative LSQR method, without ever forming the Kronecker-product matrix that vectorization would produce. Its proposal is to run the LSQR recurrence with tensors in place of vectors, storing every iterate in the tensor-train format and truncating ranks after each sum. The authors argue this is practical: memory for the iterates scales with the TT ranks rather than with the full grid size, and a randomized sketch can shrink the tall coefficient matrices. In experiments on three term-document corpora and on Fashion-MNIST images, the resulting solver, used with two tensor-based classification criteria, gives success rates that are competitive with, and for the simple matrix baseline usually better than, standard query-matching and projection methods. A sympathetic reader would take the paper's core claim to be that problems of this form are now accessible to a memory-saving iterative solver, and that this solver is accurate enough to be useful in data mining.

What carries the argument

The load-bearing object is the tensor-train (TT) decomposition, which writes a $d$-dimensional tensor as a chain of small cores, $\mathcal{X}(i_1,\dots,i_d)=G_1(i_1)G_2(i_2)\cdots G_d(i_d)$ with $r_0=r_d=1$, so storage scales with the TT ranks instead of with the full multidimensional grid. The algorithm that carries the argument is the LSQR recurrence itself: vectors become tensors, the coefficient operator applies the sum of Kronecker products mode by mode without forming the products explicitly, and TT-SVD rounding after each sum keeps the ranks bounded. Two accelerants complete the machinery: a preconditioner built from the upper-triangular QR factors of selected coefficient matrices, and a randomized sketching operator that projects each mode's matrix onto a much smaller row space, approximately preserving Euclidean distances, before the iteration starts.

What would settle it

On a small instance of the multiterm tensor least-squares problem where the unrounded vectorized LSQR minimizer can be computed exactly, run TT-LSQR with no rounding and with a sequence of looser rounding tolerances; if the rounded solution errors do not tend to the unrounded solution as the tolerance tends to zero, or if the residual stops decreasing at a level inconsistent with the tolerance, the central claim fails.

Watch

Extended reading notes

Core claim

On its own terms, the central discovery is that the LSQR recurrence is format-agnostic: replacing the vectors by tensors and the operator by $\mathcal{L}(\mathcal{X})=\sum_i \mathcal{X} \times_1 A_1^{(i)} \cdots \times_d A_d^{(i)}$ yields exactly the same iterates as the vectorized method before any rounding is applied. Because sums of tensor-train tensors have ranks equal to the sum of the addend ranks, the paper applies TT-SVD rounding after each addition and application of $\mathcal{L}$, at the cost of a per-step error controlled by the rounding tolerance. It then shows that this truncated tensor LSQR, optionally preceded by QR-based right preconditioning and applied to a randomized sketch of each mode, solves the multiterm problem and produces classification decisions through two criteria: a direct residual criterion and a subspace-projection criterion built from the singular vectors of the TT-cores. The paper's claim is that this combination is a workable solver and a competitive tool for allocating new documents or images to existing clusters.

Load-bearing premise

The method rests on the assumption that repeatedly compressing the tensor-train representation after each update does not carry the iterates away from the true least-squares solution; the paper validates the per-step truncation error but does not analyze how these errors accumulate over hundreds of iterations.

Editorial extensions

If this is right

  • Multiterm tensor least-squares problems with three or more modes become solvable without forming or storing the Kronecker-product coefficient matrix, whose size would be infeasible.
  • Truncation gives a controllable trade-off: looser TT rounding tolerances or smaller rank caps make the iterates stagnate at predictable residual levels, matching the behavior known for truncated matrix Krylov methods.
  • For fixed total training data, splitting it into more terms $\ell$ with fewer columns $m$ per term lowers CPU time dramatically while keeping classification accuracy roughly constant.
  • Sketching the keyword or pixel space cuts CPU time by a large factor, and a short unsketched refinement using the sketched solution as a starting guess often recovers most of the lost accuracy.
  • The tensor-based subspace-projection criterion (C2) generally matches or beats simple matrix least-squares query matching, which is unreliable on weakly correlated clusters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference: The format-level nature of the rounding suggests the same tensorized template should transfer to other Krylov iterations, such as CG on the normal equations or GMRES, for sums of Kronecker products; the paper only develops LSQR.
  • Inference: The authors mention combining the two classification criteria as future work; a natural test is a voting rule that could stabilize classification on weakly correlated groups such as the Fashion-MNIST sandals class.
  • Inference: The sketch is applied per mode with the same sketch size; one could test mode-dependent sketch sizes, since the reported correlation patterns differ markedly across groups and datasets.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes TT-LSQR, a tensor-train implementation of the classical LSQR algorithm for the multiterm tensor least squares problem (1.1), where the coefficient is a sum of Kronecker products of tall matrices. The algorithm applies LSQR recurrences to tensors in TT format and rounds the TT-ranks after each sum. The authors also introduce a sketching variant, discuss preconditioning, and apply the method to query-document classification using two criteria (C1) and (C2) on Reuters, Cranfield, Medline, and FashionMNIST data, comparing against a matrix least squares criterion (C3) and a truncated-SVD projection criterion (C4). The central claim is that TT-LSQR provides an effective, memory-saving solver for (1.1) and that the resulting classification framework is promising.

Significance. If the main claim were fully established, the paper would contribute a practical TT-based solver for a genuinely hard class of multiterm tensor least squares problems, with a plausible application to text and image classification. The algorithmic idea is natural, the use of the TT-Toolbox makes the implementation concrete, and the sanity checks in Section 5 usefully document the effect of rounding and rank truncation. The classification criteria are simple and do not involve fitted parameters beyond the least squares solution. However, the absence of any accumulated perturbation analysis for the repeated rounding in the LSQR recurrence leaves the central numerical claim unproven, and the classification evidence rests on very small test sets. The contribution is therefore best regarded as a promising heuristic numerical study rather than a fully supported solver.

major comments (4)
  1. [Section 3, Algorithm 3.1] The central load-bearing point is that TT-LSQR solves the original problem (1.1), but the paper only states in Section 3 that after each sum 'some truncation is necessary' and that the iterates coincide with the vectorized case only 'before truncation.' No result controls the cumulative effect of rounding U_{i+1}, V_{i+1}, and X_i at every iteration; Theorem 3.1 bounds only a single TT-SVD rounding step. Once rounding is applied, the scalars alpha_i, beta_i, rho_i, and theta_i no longer describe a fixed linear operator, so the classical LSQR convergence theory of [32] does not apply, and the method may converge to a tolerance- and rank-dependent problem rather than to the minimizer of (1.1). Please provide an accumulated perturbation bound, a low-rank representability condition on the true minimizer, or explicitly reframe the contribution as a heuristic rank-constrained solver with empirical validation only.
  2. [Section 5, Figure 5.1] The sanity check on the discretized PDE reports only relative residual norms and shows that stagnation is controlled by the truncation threshold. This does not establish that the computed iterates are close to the true solution of (5.1) or to the least squares minimizer of the original problem, since the residual may stagnate at a nonzero value for a different rounded problem. Please include an error measure against the exact solution or against an unconverged reference solution of the full problem, and report the TT-ranks achieved during the iterations.
  3. [Section 7.2, Tables 7.1-7.4] The classification experiments use 20 test documents per category (40 for FashionMNIST), and the authors themselves note that a 5% difference is a single document. Consequently, many of the reported differences between criteria (C1) and (C2) or between values of bar m are not statistically meaningful, and several claims such as 'a general preference of criterion (C2) over (C1)' are not supported at this granularity. Please provide confidence intervals, repeated train/test splits, or larger test sets, and restrict the qualitative conclusions to differences that survive this uncertainty.
  4. [Section 4.2, Eq. (4.1)] The sketching construction is not fully specified. If bA_j^{(i)} = S(A_j^{(i)}) with S: R^n -> R^s, then the sketched Kronecker factor has s^d rows, while S(f) as defined maps a single mode to length s; the notation in (4.1) is therefore ambiguous unless S is applied modewise to the whole tensor F. In addition, the chosen sketch dimension s = 2d bar m is far below the s ~ n log n / epsilon^2 required by the cited Johnson-Lindenstrauss bound, so that bound does not justify the reported accuracy. Please define the action of S on f explicitly, justify the sketch dimension, and report the relative residual of the original (unsketched) problem for the sketched solutions.
minor comments (5)
  1. [Section 8] The sentence 'the conclusions are drown' contains a typo; it should read 'drawn.'
  2. [Section 7.1, Criterion (C1)] The notation in Criterion (C1), in particular the expression '1 (x)_j f (x) 1' and the accompanying footnote, is unclear as printed; please define the positioning of f in the Kronecker product with a concrete formula.
  3. [Section 3.1, Theorem 3.1] The theorem is cited as [30], which is the TT-cross paper by Oseledets and Tyrtyshnikov, whereas the stated TT-SVD error estimate is usually attributed to [28]; please verify and correct the citation.
  4. [Table 7.5] For the case ell = 3 the table reports results on only 10 test documents while the other rows use 20 documents; this difference should be stated directly in the table caption or in the surrounding text, since it affects the interpretability of the CPU-time comparison.
  5. [Section 3, code availability] The text says the code 'will be made available' at a GitHub repository, but no repository link or release is provided; please include the link or state clearly that the code is available upon request.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: TT-LSQR is an independent algorithmic adaptation, and the truncation gap is a correctness concern, not a definitional reduction.

full rationale

The paper's central claim is an algorithmic implementation (TT-LSQR) plus experimental classification criteria. The derivation chain is: vectorized LSQR, tensor-reshaped iteration, TT rounding after each sum, and classification criteria C1/C2. None of these steps reduces to its own input by construction. The statement that iterates before truncation coincide with vectorized LSQR is true by the mode-product/Kronecker correspondence, and the paper explicitly acknowledges that truncation changes the iterates ('some truncation is necessary'), so no prediction is disguised as a fit. Theorem 3.1 bounds a single TT-SVD rounding and is cited from Oseledets and Tyrtyshnikov; it is external and not a self-citation. The only same-author citation, [34] (matrix truncated LSQR), is used as a template and comparison method, but the tensor implementation and the classification experiments are self-contained and tested against external benchmarks; no load-bearing theorem is imported by self-citation. The lack of an accumulated perturbation bound for repeated rounding is a genuine mathematical gap in the paper's convergence theory, but a gap is not circularity: the algorithm's output is not defined to be the classification result, and criteria C1/C2 are evaluated rather than fitted. Accordingly, score 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The method's convergence depends on an unproven interaction between rounding and LSQR; the application relies on an ad hoc tensor model. The only independent inputs from prior literature are the TT-SVD error bound and the classical LSQR algorithm.

free parameters (6)
  • TT rounding tolerance = 10^-4 in classification; 10^-9, 10^-7, 10^-5, 10^-3 in PDE tests
    Hand-chosen truncation threshold; Figure 5.1 shows the residual stagnation level tracks this parameter.
  • Number of TT-LSQR iterations = 10 for classification; 200-600 for PDE tests
    Stopping is fixed a priori, not by a convergence criterion, for the data mining experiments; the output depends on this choice.
  • Sketching dimension s = s = 2*d*bar_m
    Selected ad hoc; the quoted theoretical bound in Section 4.2 requires s of order n log n / eps^2, which is far larger.
  • Max TT-rank used in rounding = 20, 30, 40, 50 in PDE experiments
    User-specified caps on TT-ranks; Figure 5.1 (right) shows their effect on convergence.
  • Number of terms ell and number of modes d = ell = 6, d = 3
    Application-specific choices; Table 7.5 shows CPU time and classification change substantially when ell and m vary.
  • Number of singular triplets in baseline C4 = 10
    Used for the comparison method, not part of the proposed algorithm; the choice is not justified.
assumptions (4)
  • standard math TT-SVD truncation error bound (Theorem 3.1)
    Quoted from Oseledets and Tyrtyshnikov [30]; used to justify the accuracy of rounding.
  • domain assumption Rounding at each TT-LSQR iteration preserves a meaningful approximation of the least squares solution
    No convergence analysis is provided; the paper relies on TT-SVD error control and a single PDE sanity check (Section 5), but accumulated truncation error is not bounded.
  • ad hoc to paper The tensor model with F = f tensor f tensor f and partitioned term-document matrices is a valid representation for query classification
    Introduced in Section 7.1 without statistical justification; the categories are defined by K-means on the same data, so the model is not independently validated.
  • domain assumption The mode-wise preconditioner chosen as the R factor with lowest condition number is effective for the whole multiterm problem
    Heuristic stated in Section 4.1; no analysis or extensive validation of the preconditioner's impact is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of TT-LSQR For Tensor Least Squares Problems and Application to Data Mining *." pith.science (2026). https://pith.science/paper/7PIQVCC6

@misc{pith2026250201293,
  author       = {Pith},
  title        = {Pith review of: TT-LSQR For Tensor Least Squares Problems and Application to Data Mining *},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7PIQVCC6}},
  note         = {Machine review of arXiv:2502.01293}
}
abstract

We are interested in the numerical solution of the tensor least squares problem \[ \min_{\mathcal{X}} \| \mathcal{F} - \sum_{i =1}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \times_2 A_2^{(i)} \cdots \times_d A_d^{(i)} \|_F, \] where $\mathcal{X}\in\mathbb{R}^{m_1 \times m_2 \times \cdots \times m_d}$, $\mathcal{F}\in\mathbb{R}^{n_1\times n_2 \times \cdots \times n_d}$ are tensors with $d$ dimensions, and the coefficients $A_j^{(i)}$ are tall matrices of conforming dimensions. We first describe a tensor implementation of the classical LSQR method by Paige and Saunders, using the tensor-train representation as key ingredient. We also show how to incorporate sketching to lower the computational cost of dealing with the tall matrices $A_j^{(i)}$. We then use this methodology to address a problem in information retrieval, the classification of a new query document among already categorized documents, according to given keywords.

Figures

Figures reproduced from arXiv: 2502.01293 by the authors.

Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

38 extracted references · 37 canonical work pages

  1. [32]

    C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear equations and sparse 20 least squares, ACM Transactions on Mathematical Software (TOMS), 8 (1982), pp. 43–71

    work page 1982

  2. [1]

    R. D. Algarte, Tensor-based foundations of ordinary least squares and neural network regres- sion models, 2025

    work page 2025

  3. [2]

    A. H. Bentbib, A. Khouia, and H. Sadok, The LSQR method for solving tensor least-squares problems, Electronic Transactions on Numerical Analysis, 55 (2022), pp. 92–111. 19

    work page 2022

  4. [3]

    Benzi and M

    M. Benzi and M. Tuma , A robust preconditioner with low memory requirements for large sparse least squares problems , SIAM J. on Scientific Computing, 25 (2003), pp. 499–512

    work page 2003

  5. [4]

    M. W. Berry and M. Browne , Understanding Searching Engines , Software, Enviroments, and Tools, SIAM, Philadelphia, USA, 1999

    work page 1999

  6. [5]

    Bouss´e, N

    M. Bouss´e, N. Vervliet, O. Debals, and L. De Lathauwer, Face recognition as a Kronecker product equation, in IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Dec. 2017, pp. 1–5

    work page 2017

  7. [6]

    Brandoni and V

    D. Brandoni and V. Simoncini , Tensor-train decomposition for image recognition , Calcolo, 57 (2020). article # 9

    work page 2020

  8. [7]

    Bucci, D

    A. Bucci, D. Palitta, and L. Robol , Randomized sketched TT-GMRES for linear systems with tensor structure , Tech. Rep. 2409.09471, arXiv, 2024

    arXiv 2024

Show all 38 references
  1. [8]

    Chang and H.-C

    S.-Y. Chang and H.-C. Wu , Tensor-based least-squares solutions for multirelational signals and applications, IEEE Transactions on Cybernetics, 54 (2024), pp. 2852–2865

    2024

  2. [9]

    Chen and D

    M. Chen and D. Kressner , Recursive blocked algorithms for linear systems with Kronecker product structure, Numerical Algorithms, 84 (2020), pp. 1199–1216

    2020

  3. [10]

    C. F. Dantas, J. E. Cohen, and R. Gribonval , Learning tensor-structured dictionaries with application to hyperspectral image denoising , in 27th European Signal Processing Confer- ence, EUSIPCO 2019, A Coru˜ na, Spain, September 2-6, 2019, IEEE, 2019, pp. 1–5

    2019

  4. [11]

    C. F. Dantas, M. N. Da Costa, and R. da Rocha Lopes , Learning dictionaries as a sum of Kronecker products, IEEE Signal Processing Letters, 24 (2017), pp. 559–563

    2017

  5. [12]

    De Lathauwer, B

    L. De Lathauwer, B. De Moor, and J. V andewalle , A multilinear singular value decom- position, SIAM J. on Matrix Analysis and Applications, 21 (2000), pp. 1253–1278

    2000

  6. [13]

    S. V. Dolgov and D. V. Savostyanov, Alternating minimal energy methods for linear systems in higher dimensions, SIAM Journal on Scientific Computing, 36 (2014), pp. A2248–A2271

    2014

  7. [14]

    Eld ´en, Matrix methods in Data Mining and Pattern Recognition , Fundamentals of Algo- rithms, SIAM, Philadelphia, USA, 2019

    L. Eld ´en, Matrix methods in Data Mining and Pattern Recognition , Fundamentals of Algo- rithms, SIAM, Philadelphia, USA, 2019. II ed

    2019

  8. [15]

    Hackbusch, B

    W. Hackbusch, B. N. Khoromskij, and E. E. Tyrtyshnikov, Hierarchical Kronecker tensor- product approximations, J. Numer. Math., 13 (2005), pp. 119–156

    2005

  9. [16]

    N. Hao, M. E. Kilmer, K. Braman, and R. C. Hoover, Facial recognition using tensor-tensor decompositions, SIAM J. on Imaging Sciences, 6 (2013), pp. 437–463

    2013

  10. [17]

    G. W. Howell and M. Baboulin, LU preconditioning for overdetermined sparse least squares problems, in Parallel Processing and Applied Mathematics, R. Wyrzykowski, E. Deelman, J. Dongarra, K. Karczewski, J. Kitowski, and K. Wiatr, eds., Cham, 2016, Springer Inter- national Publ...

    2016

  11. [18]

    Jiang, F

    B. Jiang, F. Yang, and S. Zhang , Tensor and its Tucker core: the invariance relationships , Numerical Linear Algebra with Applications, 24 (2017), p. e2086

    2017

  12. [19]

    R. A. Johnson and D. W. Wichern, Applied multivariate statistical analysis, Pearson Prentice Hall, NJ, 2007

    2007

  13. [20]

    Kernfeld, M

    E. Kernfeld, M. Kilmer, and S. Aeron, Tensor-tensor products with invertible linear trans- forms, Linear Algebra Appl., 485 (2015), pp. 545–570

    2015

  14. [21]

    B. N. Khoromskij , Tensors-structured numerical methods in scientific computing: survey on recent advances, Chemometrics and Intelligent Laboratory systems, 110 (2012), pp. 1–19

    2012

  15. [22]

    , Tensor Numerical Methods in Scientific Computing , De Gruyter, Berlin, Boston, 2018

    2018

  16. [23]

    T. G. Kolda and B. W. Bader , Tensor decompositions and applications , SIAM Review, 51 (2009), pp. 455–500

    2009

  17. [24]

    Kressner and C

    D. Kressner and C. Tobler, Krylov subspace methods for linear systems with tensor product structure, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1688–1714

    2010

  18. [25]

    Kressner and C

    D. Kressner and C. Tobler , Low-rank tensor Krylov subspace methods for parametrized linear systems, SIAM. J. Matrix Anal. & Appl., 32 (2011), pp. 1288–1316

    2011

  19. [26]

    Martinsson and J

    P.-G. Martinsson and J. A. Tropp , Randomized numerical linear algebra: Foundations and algorithms, Acta Numerica, 29 (2020), p. 403–572

    2020

  20. [27]

    Meier, Y

    M. Meier, Y. Nakatsukasa, A. Townsend, and M. Webb , Are sketch-and-precondition least squares solvers numerically stable? , SIAM J. on Matrix Analysis and Applications, 45 (2024), pp. 905–929

    2024

  21. [28]

    Oseledets, Tensor-train decomposition, SIAM J

    I. Oseledets, Tensor-train decomposition, SIAM J. Scientific Computing, 33 (2011), pp. 2295– 2317

    2011

  22. [29]

    Oseledets, TT-Toolbox, 2025

    I. Oseledets, TT-Toolbox, 2025. https://github.com/oseledets/TT-Toolbox

    2025

  23. [30]

    Oseledets and E

    I. Oseledets and E. Tyrtyshnikov , TT-cross approximation for multidimensional arrays , Linear Algebra and its Applications, 432 (2010), pp. 70–88

    2010

  24. [31]

    I. V. Oseledets and S. V. Dolgov , Solution of linear systems and matrix inversion in the TT-format, SIAM Journal on Scientific Computing, 34 (2012), pp. A2718–A2739

    2012

  25. [33]

    Palitta and V

    D. Palitta and V. Simoncini, Matrix-equation-based strategies for convection–diffusion equa- tions, BIT Numerical Mathematics, 56 (2016), pp. 751–776

    2016

  26. [34]

    Piccinini and V

    L. Piccinini and V. Simoncini, Truncated LSQR for Matrix Least Squares Problems, To appear in Computational Optimization and Applications (COAP), (2025), pp. 1–22

    2025

  27. [35]

    Rokhlin and M

    V. Rokhlin and M. Tygert , A fast randomized algorithm for overdetermined linear least- squares regression, Proc. Natl. Acad. Sci. USA, 105 (2008), pp. 13212–13217

    2008

  28. [36]

    N. A. Saputra, L. S. Riza, A. Setiawan, and I. Hamidah , A systematic review for classifi- cation and selection of deep learning methods , Decision Analytics Journal, 12 (2024)

    2024

  29. [37]

    Simoncini, Numerical solution of a class of third order tensor linear equations , Bollettino UMI, 13 (2020), pp

    V. Simoncini, Numerical solution of a class of third order tensor linear equations , Bollettino UMI, 13 (2020), pp. 429–439

    2020

  30. [38]

    D. P. Woodruff , Sketching as a tool for numerical linear algebra , Found. Trends Theor. Comput. Sci., 10 (2014), pp. 1–157. 21

    2014

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.