- Multifrontal Computation with the Orthogonal Factors of Sparse Matrices by S.-M. Lu and JB. SIAM J. Matrix Anal. Appl., 17, (1996), pp. 658-679.
- An algorithm and a stability theory for downdating the ULV decomposition by JB, P.A. Yoon, and H. Zha, BIT, 36 (1996), pp.15-40.
- P.A. Yoon and J.L. Barlow, An Efficient Rank Detection Procedure for Modifying the ULV decomposition. BIT 38(4),pp. 781--801 1998.
- JB, M.W. Berry, A. Ruhe, and H.Zha, 2nd Special Issue on Matrix Comptations and Statistics, Computational Statistics and Data Analysis, 41(2002):1
- A modified Gram-Schmidt based downdating technique fo ULV decompositions with applications to recursive TLS Problems by JB, Hasan Erbay, and Zhenyue Zhang. Computational Statistics and Data Analysis,41(1):195-211.
- An Alternative Algorithm for Refinement of ULV Decompositions by JB, H. Erbay, and I. Slapnicar, SIAM J. Matrix Anal. Appl.,27(1):198-211,2005.
- Numerical Aspects of Solving Linear Least Squares ProblemsIn Handbook of Statistics , 9:303--376. Edited by C.R. Rao,(1993).
- Modification and Maintainence of ULV Decompositions a survey paper that will appear as the proceedings of the Computational Mathematics meeting in Dubrovnik.
- Improved Gram-Schmidt type downdating methods JB, A. Smoktunowicz, and H. Erbay, BIT, 45(2): 259--285, 2005.
- H. Erbay and JB, An Alternative Algorithm for a Sliding Window ULV Decompsition, Computing, 76(1-2): 55--66,2006.
- JB, P. Groenen, H. Park, and H. Zha, 2nd Special Issue on Matrix Comptations and Statistics,. Computational Statistics and Data Analysis, 50(2006):1-4
- A. Smoktunowicz, J. Barlow, and J. Langou. A note on the error analysis of Classical Gram Schmidt, Numerische Mathematik 105:299--313
- H. Erbay and J.L. Barlow, A Modifiable Low-Rank Approximation to a Matrix, Numerical Linear Algebra with Applications,16(10):833--860,2009.
- J. Barlow and A. Smoktunowicz. Reorthogonalized block classical Gram--Schmidt. Numerische Mathematik, 123(3):395--423,2013.
- J.L. Barlow, Block Gram-Schmidt Downdating, Electronic Transactions on Numerical Analysis, 43:163--187,2014-2015.
- J.L. Barlow, Block Modified Gram-Schmidt Algorithms and Their Analysis SIAM J. Matrix Analysis and Applications, to appear, 2019.

- A Regularized Structured Total Least Squares Algorithm for High Resolution Image Reconstruction by H. Fu and JLB. Linear Algebra and Its Applications, 391:75--98,2004.
- Structured Total Least Squares for Color Image Restoration H. Fu, M. Ng, and JB, SIAM J. Scientific Computing, 28(3): 1100--1119, 2006.
- Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration by H. Fu, M.K. Ng, J.L. Barlow, and W.-K. Ching, ICCSA(4):843-851,2005.
- Efficient Minimization Methods of Mixed l1-l2 and l1-l1 Norms for Image Restoration by H. Fu, M.K. Ng, M. Nikolova, and J.L. Barlow, SIAM J. Scientific Computing, 27(6):1881-1902,2006.
- G.Lee, J.L. Barlow, and H. Fu, Fast High-resolution image reconstruction using Tikanov Regularization based Total Least Squares SIAM J. Sci. Computing, 35(1):B275--B290,2013.
- G. Lee and J.L. Barlow, Two Projection Based Methods for Regularized Total Least Squares , Linear Algebra and Its Applications,461:18--41, 2014.
- G. Lee and J.L. Barlow, Updating approximate prinicipal components with applications to template tracking Numerical Linear Algebra and Its Applications, 24(2), e2081, 2017.
- M. Almekkawy, A. Ceravi\'{c}, A. Abdou, J. He, G.Lee, and J.L. Barlow, Solving the ultrasound inverse scattering problem of inhomogenous media using different approaches of total least squares Inverse Problems in Science and Engineering, published online June 2019.

- More Accurate Bidiagonal Reduction for Computing the Singular Value Decompositon SIAM J. Matrix Anal. Appl.,23(3):761-798,2002.
- Optimal Perturbation Bounds for the Hermitian Eigenvalue Problem by JB and Ivan Slapni\v{c}ar, Linear Algebra and Its Applications 309(2000),pp.19-43.
- A new stable bidiagonal reduction algorithm JB, N. Bosner, and Z. Drmac, Linear Algebra and Its Applications,397:35-84,2005.
- N. Bosner and J. Barlow. Block and parallel versions of one-sided bidiagonalization. ,SIAM J. Matrix Anal. Appl.,29(3):927-953,2007.
- J.L. Barlow, Reorthogonalization for Golub--Kahan--Lanczos bidiagonal reduction, Numerische Mathematik, 124(2):237--278,2013
- N. Jako\v{c}evi\'{c}-Stor, I. Slapni\v{c}ar, and J.L. Barlow, Accurate eigenvalue decomposition of real symmetric arrowhead matrices and applications, Linear Algebra and Its Applications, 464:62--89,2015.
- N. Jako\v{c}evi\'{c}-Stor, I. Slapni\v{c}ar, and J.L. Barlow, Forward stable eigenvalue decomposition of rank-one modifications of diagonal matricesLinear Algebra and Its Applications, 487:301-315, 2015.

- Growth in Gaussian Elimination, Orthogonal Matrices, and the Euclidean Norm by JB and H. Zha, SIAM J. Matrix Anal. Appl., 19:807-815, 1998. .
- Stable Computation of the Fundamental Matrix of a Markov Chain by JB, SIAM J. Matrix Analysis and Applications,22(1), pp.230-241, January 2001.
- X. Yang, H. Fu, Hongyuan Zha, and J. Barlow. Semi-Supervised Nonlinear Dimensionality Reduction , Proceedings of the 23rd International Conference on Machine Learning, (ICML 2006).
- S. Yan, S. Bouaziz, D. Lee, and J.L. Barlow, Semi-supervised dimensionality reduction for analyzing High-Dimensional Data with constraints, Neurocomputing, 76(1):114--124, 2012.
- D. Di Serafino, G. Toraldo, M. Viola, and J.L. Barlow, A Two-Phase Gradient Method for Quadratic Programming Problems with a Single Variable Constraint and Bounds on the Variables SIAM J. Optimization, 28(4):2809-2838, 2018.

I am also in the process of writing a book, tentatively titled * Computational Linear Least Squares *. Drafts of
Chapters one, two, and three and a tentative table of contents
are available. Any comments are very welcome.

My resume lists all of my publications.

Back to my home page .