Jesse Barlow's Papers since 1996

Least Squares and Total Least Squares

• 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.

Numerical Algorithms for Image Processing

• 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.

Eigenvalues and Singular Values

• 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.

Other Topics

• 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.