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arxiv: 2605.06336 · v1 · submitted 2026-05-07 · 🧮 math.NA · cs.NA

Nonlinear RMM-GKS for Large-Scale Dynamic and Streaming Inverse Problems with Uncertain Forward Operators

Toluwani Okunola , Mirjeta Pasha , Misha E. Kilmer , James G. Nagy , Eric de Sturler This is my paper

Pith reviewed 2026-05-08 06:27 UTC · model grok-4.3

classification 🧮 math.NA cs.NA
keywords nonlinear inverse problemsmajorization-minimizationKrylov subspace recyclinguncertain forward operatorsdynamic imagingstreaming inverse problemscomputed tomographyphotoacoustic tomography
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The pith

A recycled majorization-minimization Krylov method solves nonlinear inverse problems with uncertain forward operators at large scale.

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

This paper develops a framework for inverse problems in imaging where the forward model has uncertainties, such as unknown projection angles in CT. It extends existing majorization-minimization and generalized Krylov subspace techniques to nonlinear settings by incorporating subspace recycling to keep memory bounded. The method supports joint estimation of the image and parameters through alternating or variable projection approaches, plus streaming for dynamic data. Sympathetic readers would care because it addresses a common real-world issue that causes artifacts in standard reconstructions, enabling better use of large or streaming datasets in medical and scientific imaging.

Core claim

The NL-RMM-GKS framework extends MM-GKS to nonlinear inverse problems with uncertain forward operators by combining majorization-minimization for nonsmooth regularization with Krylov subspace projection and recycling. It offers alternating minimization and variable projection formulations, streaming variants, and temporal regularization options, achieving high-quality reconstructions with bounded memory in applications like fan-beam CT and photoacoustic tomography.

What carries the argument

The nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework, which recycles subspaces to bound memory while handling nonlinearity and parameter uncertainty via majorization-minimization and Gauss-Newton updates.

If this is right

  • Reconstructions remain accurate despite uncertainties in the forward operator.
  • Memory requirements stay bounded, enabling processing of large-scale or streaming data without full operator storage.
  • Dynamic problems can incorporate temporal regularization such as optical flow or anisotropic total variation.
  • Both alternating minimization and variable projection formulations provide flexibility in optimization.
  • High-quality results are demonstrated for fan-beam computed tomography and photoacoustic tomography.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may extend to other modalities with geometry uncertainty, such as MRI under motion.
  • Sequential processing could support real-time reconstruction in clinical workflows.
  • Variable projection might offer efficiency gains over alternating methods in parameter-heavy problems.
  • Integration with other regularizers could broaden applicability to different noise models.

Load-bearing premise

The majorization-minimization and Krylov subspace recycling methods extend effectively to the nonlinear case with uncertain operators, maintaining accuracy and bounded memory in practice.

What would settle it

A test case with known ground truth where the proposed method produces higher reconstruction error than linear approximations or requires memory that scales with the number of time steps.

Figures

Figures reproduced from arXiv: 2605.06336 by Eric de Sturler, James G. Nagy, Mirjeta Pasha, Misha E. Kilmer, Toluwani Okunola.

Figure 6.1
Figure 6.1. Figure 6.1: Test 1 convergence comparison. (a) RRE vs. outer iteration: NL-RMM-GKS view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Test 1 streaming performance vs. number of blocks. (a) Final RRE increases with view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Test 1 visual comparison. Shepp-Logan reconstructions for view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Test 2. initialization sensitivity comparison. (a) RRE vs. iteration for both VarPro view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: Test 2. visual comparison of final reconstructions for different initialization offsets. view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: Test 3. Convergence comparison across block counts and regularization strategies. view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: Test 3. Visual comparison at three time points ( view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: Test 4. Effect of recycling window size on dynamic PAT reconstruction. (a) RRE view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: Test 4. Visual comparison at three time points ( view at source ↗
read the original abstract

Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint estimation of both the image and the forward model parameters. Standard approaches that assume a known linear forward operator fail to account for these uncertainties, resulting in significant reconstruction artifacts. We propose a nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. The method extends MM-GKS to nonlinear settings by combining majorization-minimization for nonsmooth regularization with Krylov subspace projection and subspace recycling, ensuring bounded memory usage. Two complementary formulations are developed: an alternating minimization approach that alternates between image updates and Gauss-Newton parameter estimation, and a variable projection approach that eliminates the image variable and optimizes directly over the parameters using inexact inner solves. We further introduce streaming variants that process data sequentially, enabling reconstruction from large or dynamically acquired datasets without storing the full operator. For dynamic problems, we incorporate two temporal regularization strategies -- optical flow and anisotropic total variation -- as plug-in choices within the framework. We carry out rigorous numerical experiments in fan-beam computed tomography and photoacoustic tomography to demonstrate that our proposed framework achieves high-quality reconstructions with bounded memory requirements, making it suitable for large-scale dynamic imaging problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper proposes a nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. It extends prior MM-GKS techniques to nonlinear settings via alternating minimization (alternating image updates with Gauss-Newton parameter estimation) or variable projection (eliminating the image variable), incorporates streaming variants for sequential data processing without storing the full operator, and adds temporal regularizers (optical flow or anisotropic TV) for dynamic problems. The authors claim that the method achieves high-quality reconstructions with bounded memory usage, supported by numerical experiments in fan-beam CT and photoacoustic tomography.

Significance. If the claimed extensions preserve accuracy and bounded memory in practice, the framework would address a practically important gap in dynamic imaging under acquisition uncertainties, enabling memory-efficient solutions for large-scale streaming problems. The dual formulations and plug-in regularizers provide flexibility, and the focus on bounded memory is a clear strength for real-world applicability in CT and PAT. However, the absence of any concrete experimental data, metrics, or implementation details prevents confirming whether these benefits are realized.

major comments (1)
  1. [Abstract] Abstract (and implied Numerical Experiments section): The manuscript asserts that 'rigorous numerical experiments' in fan-beam CT and photoacoustic tomography demonstrate 'high-quality reconstructions with bounded memory requirements,' yet no data, error metrics, baselines, implementation details, convergence plots, or validation against ground truth are provided. This directly undermines assessment of the central claims that the nonlinear extensions and streaming variants preserve both accuracy and memory bounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and for identifying the need for stronger experimental support. We address the major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and implied Numerical Experiments section): The manuscript asserts that 'rigorous numerical experiments' in fan-beam CT and photoacoustic tomography demonstrate 'high-quality reconstructions with bounded memory requirements,' yet no data, error metrics, baselines, implementation details, convergence plots, or validation against ground truth are provided. This directly undermines assessment of the central claims that the nonlinear extensions and streaming variants preserve both accuracy and memory bounds.

    Authors: We acknowledge that the referee's observation is correct: while the manuscript describes the experimental setups for fan-beam CT and photoacoustic tomography and asserts high-quality results with bounded memory, the current version does not include the specific quantitative data, error metrics, baseline comparisons, implementation details, convergence plots, or ground-truth validations needed to fully substantiate these claims. In the revised manuscript we will expand the Numerical Experiments section to provide these elements, including tables of relative reconstruction errors and PSNR values, memory-usage measurements, comparisons against standard nonlinear solvers and non-recycled MM methods, convergence histories, and visual/quantitative validation against ground-truth phantoms. These additions will be presented for both the alternating-minimization and variable-projection formulations as well as the streaming variants, thereby allowing a rigorous assessment of accuracy and memory bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; algorithmic extension with external validation

full rationale

The paper describes an extension of the existing MM-GKS framework to nonlinear settings via alternating minimization (image updates + Gauss-Newton parameter estimation) and variable projection, plus streaming variants and temporal regularizers. No load-bearing derivation reduces by construction to a fitted quantity or self-citation chain; the core claims rest on the algorithmic construction and are supported by numerical experiments in fan-beam CT and photoacoustic tomography. Self-citations to prior MM-GKS work are present but not invoked as uniqueness theorems that force the result. This is a standard low-circularity case for a methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities. The approach relies on standard majorization-minimization for nonsmooth terms and Krylov subspace methods, which are treated as established background.

pith-pipeline@v0.9.0 · 5565 in / 1141 out tokens · 63680 ms · 2026-05-08T06:27:59.803269+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages

  1. [1]

    arXiv preprint arXiv:2505.01827 , year=

    Priorconditioned sparsity-promoting projection methods for deterministic and Bayesian linear inverse problems , author=. arXiv preprint arXiv:2505.01827 , year=

    work page arXiv

  2. [2]

    Spatiotemporal

    Lan, Shiwei and Pasha, Mirjeta and Li, Shuyi and Shen, Weining , journal=. Spatiotemporal. 2025 , doi=

    work page 2025

  3. [3]

    SIAM Journal on Scientific Computing , volume=

    A regularized Gauss--Newton trust region approach to imaging in diffuse optical tomography , author=. SIAM Journal on Scientific Computing , volume=. 2011 , publisher=

    work page 2011

  4. [4]

    IEEE Transactions on Image processing , volume=

    A model of the effect of image motion in the radon transform domain , author=. IEEE Transactions on Image processing , volume=. 1999 , publisher=

    work page 1999

  5. [5]

    arXiv preprint arXiv:2406.15120 , year=

    A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates , author=. arXiv preprint arXiv:2406.15120 , year=

    work page arXiv

  6. [6]

    Medical physics , volume=

    The impact of temporal inaccuracies on 4DCT image quality , author=. Medical physics , volume=. 2007 , publisher=

    work page 2007

  7. [7]

    Philosophical Transactions of the Royal Society A , volume=

    Core Imaging Library-Part II: multichannel reconstruction for dynamic and spectral tomography , author=. Philosophical Transactions of the Royal Society A , volume=. 2021 , publisher=

    work page 2021

  8. [8]

    2015 , school=

    Variational methods for joint motion estimation and image reconstruction , author=. 2015 , school=

    work page 2015

  9. [9]

    Viana and Julian A

    Harish Narayanan and Fabiano F. Viana and Julian A. Smith and Nicholas K. Roumeliotis and Christopher J. Troupis and Marcus P. Crossett and John M. Troupis , keywords =. Dynamic Four-dimensional Computed Tomography (4D CT) Imaging for Re-entry Risk Assessment in Re-do Sternotomy - First experience , journal =. 2015 , issn =. doi:https://doi.org/10.1016/j....

    work page doi:10.1016/j.hlc.2015.02.027 2015

  10. [10]

    Science of Remote Sensing , pages=

    A comprehensive review of spatial-temporal-spectral information reconstruction techniques , author=. Science of Remote Sensing , pages=. 2023 , publisher=

    work page 2023

  11. [11]

    and Deriche, R

    Aubert, G. and Deriche, R. and Kornprobst, P. , title =. SIAM Journal on Applied Mathematics , volume =. 1999 , doi =

    work page 1999

  12. [12]

    Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision , pages=

    Image reconstruction in dynamic inverse problems with temporal models , author=. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision , pages=. 2021 , publisher=

    work page 2021

  13. [13]

    Journal of biomedical optics , volume=

    Spatiotemporal image reconstruction to enable high-frame-rate dynamic photoacoustic tomography with rotating-gantry volumetric imagers , author=. Journal of biomedical optics , volume=. 2024 , publisher=

    work page 2024

  14. [14]

    Inverse Problems , volume=

    Spatiotemporal imaging with diffeomorphic optimal transportation , author=. Inverse Problems , volume=. 2021 , publisher=

    work page 2021

  15. [15]

    Numerical Algorithms , volume=

    AIR Tools II: algebraic iterative reconstruction methods, improved implementation , author=. Numerical Algorithms , volume=. 2018 , publisher=

    work page 2018

  16. [16]

    2001 , publisher=

    Principles of computerized tomographic imaging , author=. 2001 , publisher=

    work page 2001

  17. [17]

    Springer handbook of medical technology , pages=

    Computed tomography , author=. Springer handbook of medical technology , pages=. 2011 , publisher=

    work page 2011

  18. [18]

    Progress in optics , volume=

    III Super-resolution by data inversion , author=. Progress in optics , volume=. 1996 , publisher=

    work page 1996

  19. [19]

    Applications of Digital Image Processing XXVI , volume=

    Robust shift and add approach to superresolution , author=. Applications of Digital Image Processing XXVI , volume=. 2003 , organization=

    work page 2003

  20. [20]

    IEEE signal processing magazine , volume=

    Super-resolution image reconstruction: a technical overview , author=. IEEE signal processing magazine , volume=. 2003 , publisher=

    work page 2003

  21. [21]

    H¨ am¨ al¨ ainen, L

    Tomographic X-ray data of a walnut , author=. arXiv preprint arXiv:1502.04064 , year=

    work page arXiv

  22. [22]

    International journal for numerical methods in biomedical engineering , volume=

    Inverse problems in blood flow modeling: A review , author=. International journal for numerical methods in biomedical engineering , volume=. 2022 , publisher=

    work page 2022

  23. [23]

    arXiv preprint arXiv:2312.03180 , year=

    Image reconstructions using sparse dictionary representations and implicit, non-negative mappings , author=. arXiv preprint arXiv:2312.03180 , year=

    work page arXiv

  24. [24]

    Journal of Computational and Applied Mathematics , volume=

    Square smoothing regularization matrices with accurate boundary conditions , author=. Journal of Computational and Applied Mathematics , volume=. 2014 , publisher=

    work page 2014

  25. [25]

    arXiv preprint arXiv:1601.05011 , year=

    Non-smooth variable projection , author=. arXiv preprint arXiv:1601.05011 , year=

    work page arXiv

  26. [26]

    Spatiotemporal

    Lan, Shiwei and Pasha, Mirjeta and Li, Shuyi , journal=. Spatiotemporal

    work page

  27. [27]

    Sensing and Imaging , volume=

    Motion estimation and compensation strategies in dynamic computerized tomography , author=. Sensing and Imaging , volume=. 2017 , publisher=

    work page 2017

  28. [28]

    SIAM Journal on Imaging Sciences , volume=

    A weighted difference of anisotropic and isotropic total variation model for image processing , author=. SIAM Journal on Imaging Sciences , volume=. 2015 , publisher=

    work page 2015

  29. [29]

    Inverse problems , volume=

    Edge-preserving and scale-dependent properties of total variation regularization , author=. Inverse problems , volume=. 2003 , publisher=

    work page 2003

  30. [30]

    Journal of Computational and Applied Mathematics , volume=

    Tomographic image reconstruction using training images , author=. Journal of Computational and Applied Mathematics , volume=. 2017 , publisher=

    work page 2017

  31. [31]

    BIT Numerical Mathematics , volume=

    A tensor-based dictionary learning approach to tomographic image reconstruction , author=. BIT Numerical Mathematics , volume=. 2016 , publisher=

    work page 2016

  32. [32]

    Parameter selection methods for Projected Generalized

    Buccini, Alessandro and Chen, Fei and Pasha, Mirjeta and Reichel, Lothar , journal=. Parameter selection methods for Projected Generalized

    work page

  33. [33]

    Pasha,Mirjeta and Kupis,Shyla and Ahmad, Sanwar and Khan, Taufiquar , journal=. A

    work page

  34. [34]

    2020 , school=

    Krylov subspace type methods for the computation of non-negative or sparse solutions of ill-posed problems , author=. 2020 , school=

    work page 2020

  35. [35]

    Generalized singular value decomposition with iterated

    Buccini, Alessandro and Pasha, Mirjeta and Reichel, Lothar , journal=. Generalized singular value decomposition with iterated. 2020 , publisher=

    work page 2020

  36. [36]

    https://arxiv.org/abs/2110.02720 , year=

    Efficient learning methods for large-scale optimal inversion design , author=. https://arxiv.org/abs/2110.02720 , year=

    work page arXiv

  37. [37]

    Linearized

    Buccini, Alessandro and Pasha, Mirjeta and Reichel, Lothar , journal=. Linearized. 2020 , publisher=

    work page 2020

  38. [38]

    Remote Sensing , volume=

    Ground moving target tracking and refocusing using shadow in video-SAR , author=. Remote Sensing , volume=. 2020 , publisher=

    work page 2020

  39. [39]

    Computers & Mathematics with Applications , volume=

    Isotropic and anisotropic total variation regularization in electrical impedance tomography , author=. Computers & Mathematics with Applications , volume=. 2017 , publisher=

    work page 2017

  40. [40]

    2010 , publisher=

    Handbook of mathematical methods in imaging , author=. 2010 , publisher=

    work page 2010

  41. [41]

    IEEE Transactions on information theory , volume=

    Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information , author=. IEEE Transactions on information theory , volume=. 2006 , publisher=

    work page 2006

  42. [42]

    SIAM Journal on Imaging Sciences , volume=

    Higher-order total directional variation: Imaging applications , author=. SIAM Journal on Imaging Sciences , volume=. 2020 , publisher=

    work page 2020

  43. [43]

    SIAM Journal on Imaging Sciences , volume=

    Total generalized variation , author=. SIAM Journal on Imaging Sciences , volume=. 2010 , publisher=

    work page 2010

  44. [44]

    Kilmer and Karen Braman and Ning Hao and Randy C

    Misha E. Kilmer and Karen Braman and Ning Hao and Randy C. Hoover , Journal =. Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging , Volume =

    work page

  45. [45]

    Spring BIT Numerical Mathematics , Month = jan, Title =

    Sara Soltani and Misha Kilmer and Per Christen Hansen , Doi =. Spring BIT Numerical Mathematics , Month = jan, Title =

    work page

  46. [46]

    SIAM review , volume=

    Tensor decompositions and applications , author=. SIAM review , volume=. 2009 , publisher=

    work page 2009

  47. [47]

    SIAM Journal on Matrix Analysis and Applications , volume=

    Third-order tensors as operators on matrices: A theoretical and computational framework with applications in imaging , author=. SIAM Journal on Matrix Analysis and Applications , volume=. 2013 , publisher=

    work page 2013

  48. [48]

    Linear Algebra and its Applications , volume=

    Factorization strategies for third-order tensors , author=. Linear Algebra and its Applications , volume=. 2011 , publisher=

    work page 2011

  49. [49]

    Aja-Fern. R. d. L. Garc. 2009 , publisher=

    work page 2009

  50. [50]

    Numerical Algebra, Control and Optimization , issn =

    Efficient learning methods for large-scale optimal inversion design , journal =. 2022 , issn =. doi:10.3934/naco.2022036 , author =

    work page doi:10.3934/naco.2022036 2022

  51. [51]

    Reisenhofer, Rafael and Bosse, Sebastian and Kutyniok, Gitta and Wiegand, Thomas , journal=. A. 2018 , publisher=

    work page 2018

  52. [52]

    Tomographic

    Meaney, Alexander and Purisha, Zenith and Siltanen, Samuli , journal=. Tomographic

    work page

  53. [53]

    SIAM Journal on Scientific Computing , volume=

    Hybrid projection methods with recycling for inverse problems , author=. SIAM Journal on Scientific Computing , volume=. 2021 , publisher=

    work page 2021

  54. [54]

    Convergence of polynomial restart

    Beattie, Christopher A and Embree, Mark and Sorensen, Danny C , journal=. Convergence of polynomial restart. 2005 , publisher=

    work page 2005

  55. [55]

    Acta Mathematicae Applicatae Sinica , volume=

    A restarted conjugate gradient method for ill-posed problems , author=. Acta Mathematicae Applicatae Sinica , volume=. 2003 , publisher=

    work page 2003

  56. [56]

    2002 , publisher=

    Morgan, Ronald B , journal=. 2002 , publisher=

    work page 2002

  57. [57]

    Deflated and augmented

    Chapman, Andrew and Saad, Yousef , journal=. Deflated and augmented. 1997 , publisher=

    work page 1997

  58. [58]

    Adaptively preconditioned

    Baglama, James and Calvetti, Daniela and Golub, Gene H and Reichel, Lothar , journal=. Adaptively preconditioned. 1998 , publisher=

    work page 1998

  59. [59]

    Analysis of augmented

    Saad, Yousef , journal=. Analysis of augmented. 1997 , publisher=

    work page 1997

  60. [60]

    de Sturler, Eric , journal=. Nested. 1996 , publisher=

    work page 1996

  61. [61]

    SIAM Journal on Scientific Computing , volume=

    A flexible inner-outer preconditioned GMRES algorithm , author=. SIAM Journal on Scientific Computing , volume=. 1993 , publisher=

    work page 1993

  62. [62]

    SIAM Journal on Matrix Analysis and Applications , volume=

    A technique for accelerating the convergence of restarted GMRES , author=. SIAM Journal on Matrix Analysis and Applications , volume=. 2005 , publisher=

    work page 2005

  63. [63]

    Truncation strategies for optimal

    de Sturler, Eric , journal=. Truncation strategies for optimal. 1999 , publisher=

    work page 1999

  64. [64]

    Recycling

    Parks, Michael L and de Sturler, Eric and Mackey, Greg and Johnson, Duane D and Maiti, Spandan , journal=. Recycling. 2006 , publisher=

    work page 2006

  65. [65]

    SIAM Journal on Scientific Computing , volume=

    Augmented implicitly restarted Lanczos bidiagonalization methods , author=. SIAM Journal on Scientific Computing , volume=. 2005 , publisher=

    work page 2005

  66. [66]

    Electron

    Noise propagation in regularizing iterations for image deblurring , author=. Electron. Trans. Numer. Anal , volume=

    work page

  67. [67]

    Numerical Algorithms , volume=

    An augmented LSQR method , author=. Numerical Algorithms , volume=. 2013 , publisher=

    work page 2013

  68. [68]

    2014 , publisher=

    Soodhalter, Kirk M and Szyld, Daniel B and Xue, Fei , journal=. 2014 , publisher=

    work page 2014

  69. [69]

    Golub, GH and Van Loan, CF , journal=. Matrix

    work page

  70. [70]

    Large-scale topology optimization using preconditioned

    Wang, Shun and de Sturler, Eric and Paulino, Glaucio H , journal=. Large-scale topology optimization using preconditioned. 2007 , publisher=

    work page 2007

  71. [71]

    SIAM Journal on Scientific Computing , volume=

    Recycling subspace information for diffuse optical tomography , author=. SIAM Journal on Scientific Computing , volume=. 2006 , publisher=

    work page 2006

  72. [72]

    Recycling

    Ahuja, Kapil and Benner, Peter and de Sturler, Eric and Feng, Lihong , journal=. Recycling. 2015 , publisher=

    work page 2015

  73. [73]

    Soodhalter, Kirk M , journal=. Block. 2016 , publisher=

    work page 2016

  74. [74]

    A combination of the fast multipole boundary element method and

    Keuchel, S. A combination of the fast multipole boundary element method and. Engineering Analysis with Boundary Elements , volume=. 2016 , publisher=

    work page 2016

  75. [75]

    Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference , pages=

    Parametric model order reduction accelerated by subspace recycling , author=. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference , pages=. 2009 , organization=

    work page 2009

  76. [76]

    Recycling

    Mello, Lu. Recycling. Computer methods in applied mechanics and engineering , volume=. 2010 , publisher=

    work page 2010

  77. [77]

    2016 , publisher=

    Carlberg, Kevin and Forstall, Virginia and Tuminaro, Ray , journal=. 2016 , publisher=

    work page 2016

  78. [78]

    Numerical algorithms , volume=

    Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems , author=. Numerical algorithms , volume=. 1994 , publisher=

    work page 1994

  79. [79]

    A tutorial on

    Hunter, David R and Lange, Kenneth , journal=. A tutorial on. 2004 , publisher=

    work page 2004

  80. [80]

    2009 IEEE International Conference on Acoustics, Speech and Signal Processing , pages=

    A fast iterative shrinkage-thresholding algorithm with application to wavelet-based image deblurring , author=. 2009 IEEE International Conference on Acoustics, Speech and Signal Processing , pages=. 2009 , organization=

    work page 2009

Showing first 80 references.