Jesse Barlow's Recent Papers

Below are my recently completed papers.

• 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.
• Stable chasing algorithms for modifying the complete and partial singular value decompositions by JB, P.A. Yoon, and H. Zha. A version including tedious error analysis proofs is also available .
• P.A. Yoon and J.L. Barlow, An Efficient Rank Detection Procedure for Modifying the ULV decomposition. BIT 28(4),pp. 781--801 1998.
• 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, to appear, SIAM J. Matrix Analysis and Applications,22(1), pp.230-241, January 2001.
• More Accurate Bidiagonal Reduction for Computing the Singular Value Decompositon it appeared in SIAM J. Matrix Anal. Appl.,23(3):761-798, and, for the error analysis junkie, with the tedious error analysis proof
• 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. An older version with generalized SVD bounds is also available.
• 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. Earlier version with proofs
• Numerical Aspects of Solving Linear Least Squares ProblemsIn Handbook of Statistics , 9:303--376. Edited by C.R. Rao,(1993). This is a somewhat dated survey paper that I have used as a starting point for my book.
• Modification and Maintainence of ULV Decompositions a survey paper that will appear as the proceedings of the Computational Mathematics meeting in Dubrovnik.
• 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.
• A new stable bidiagonal reduction algorithm JB, N. Bosner, and Z. Drmac, Linear Algebra and Its Applications,397:35-84,2005.
• Improved Gram-Schmidt type downdating methods JB, A. Smoktunowicz, and H. Erbay, BIT, 45(2): 259--285, 2005.
• Structured Total Least Squares for Color Image Restoration H. Fu, M. Ng, and JB, SIAM J. Scientific Computing, 28(3): 1100--1119, 2006.
• 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.
• 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. This is a link directly to Springer Link
• 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. This is a link directly to the SIAM online publication.
• 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).
• A. Smoktunowicz, J. Barlow, and J. Langou. A note on the error analysis of Classical Gram Schmidt< appeared electronically, Numerische Mathematik 105:299--313 This is the link to Springer publications.
• N. Bosner and J. Barlow. Block and parallel versions of one-sided bidiagonalization.,SIAM J. Matrix Anal. Appl.,29(3):927-953,2007.
• Reorthogonalization for Golub--Kahan--Lanczos bidiagonal reduction submitted for publication.
• J. Barlow and A. Smoktunowicz. Reorthogonalized block classical Gram--Schmidt submitted for publication.

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.