Papers

T. Wentworth and I.C.F. Ipsen:  
Kappa_SQ: A Matlab Package for Randomized Sampling of Matrices with orthonormal columns
(2014)   arXiv:1402.0642

   I.C.F. Ipsen and T. Wentworth:  
Sensitivity of Leverage Scores
(2014)   arXiv:1402.0957v1

   John T. Holodnak and I.C.F. Ipsen:  
Randomized Matrix Multiplication: Exact Computation, and Probabilistic Bounds
submitted for publication (2013)   arXiv:1310.1502

   I.C.F. Ipsen and T. Wentworth:  
Sensitivity of Leverage Scores and Coherence for Randomized Matrix Algorithms
Extended abstract, Workshop on Advances in Matrix Functions and Matrix Equations, Manchester, UK, 10-12 April 2013

   I.C.F. Ipsen and T. Wentworth:  
The Effect of Coherence on Sampling from Matrices with Orthonormal Columns, and Preconditioned Least Squares Problems
submitted for publication (2012)   arXiv:1203.4809v2
Matlab code: kappa_SQ_v3
First version: paper, kappaSQ

   S. Eriksson-Bique, M. Solbrig, M. Stefanelli, S. Warkentin, R. Abbey, and I.C.F. Ipsen:  
Importance Sampling for a Monte Carlo Matrix Multiplication Algorithm, with Application to Information Retrieval
SIAM J. Sci. Comput., vol. 33, no. 4, pp 1689-1706 (2011)

   C.T. Kelley, I.C.F. Ipsen and S.R. Pope:   Rank-Deficient and Ill-Conditioned Nonlinear Least Squares Problems
Proc. 2010 East Asian SIAM Conference, to appear

   R. Rehman and I.C.F. Ipsen:   La Budde's Method for Computing Characteristic Polynomials
arXiv:1104.3769v1

   R. Rehman and I.C.F. Ipsen:   Computing Characteristic Polynomials from Eigenvalues
SIAM J. Matrix Anal. Appl., vol. 32, no. 1, pp 90-114 (2011)

   I.C.F. Ipsen:   The Eigenproblem and Invariant Subspaces: Perturbation Theory
in G.W. Stewart: Selected Works with Commentaries, Kilmer, M. E. and O'Leary, D. P., eds, Birkhäuser, pp 71-93 (2010)

   I.C.F. Ipsen, C.T. Kelley, S.R. Pope:  Rank-Deficient Nonlinear Least Squares Problems and Subset Selection
SIAM J. Numer. Anal., vol. 49, no. 3, pp 1244-1266 (2011)

   M.E. Broadbent, M. Brown, and K. Penner (advisors: I.C.F. Ipsen and R. Rehman):   Subset Selection Algorithms: Randomized vs. Deterministic
SIAM Undergraduate Research Online, vol. 3, 22 pages (May 2010)

   I.C.F. Ipsen and T.M. Selee:   Ergodicity Coefficients Defined by Vector Norms
SIAM J. Matrix Anal. Appl., vol. 32, no. 1, pp 153-200 (2011)

   I.C.F. Ipsen and B. Nadler:   Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices
SIAM J. Matrix Anal. Appl., vol. 31, no. 1, pp 40-53 (2009)

   R.S. Wills and I.C.F. Ipsen:  Ordinal Ranking for Google's PageRank
SIAM J. Matrix Anal. Appl., vol. 30, no. 4, pp 1677-1696 (2009)

   I.C.F. Ipsen and R. Rehman:   Perturbation Bounds for Determinants and Characteristic Polynomials
SIAM J. Matrix Anal. Appl., vol. 30, no. 2, pp 762-776 (2008)

   I.C.F. Ipsen and T. M. Selee:   PageRank Computation, with Special Attention to Dangling Nodes
SIAM J. Matrix Anal. Appl., vol. 29, no. 4, pp 1281-1296 (2007)

   K.I. Dickson, C.T. Kelley, I.C.F. Ipsen and I.G. Kevrekidis:  Condition Estimates for Pseudo-Arclength Continuation
SIAM J. Numer. Anal., vol. 45, no. 1, pp 263-276 (2007)

   I.C.F. Ipsen and R.S. Wills:   Mathematical Properties and Analysis of Google's PageRank
Bol. Soc. Esp. Mat. Apl., vol. 34, pp 191-196 (2006)

   D.E. Finkel, C. Kuster, M. Lasater, R. Levy, J.P. Reese and I.C.F. Ipsen:  Communicating Applied Mathematics: Four Examples
SIAM Rev., vol. 48, no. 2, pp 359-389 (2006)

   I.C.F. Ipsen and S. Kirkland:  Convergence Analysis of a PageRank Updating Algorithm by Langville and Meyer
SIAM J. Matrix Anal. Appl., vol. 27, no. 4, pp 952-67 (2006)

   I.C.F. Ipsen and D.J. Lee:   Determinant Approximations
arXiv:1105.0437v1

   I.C.F. Ipsen:  Accurate Eigenvalues for Fast Trains
SIAM News, vol. 37, no. 9, pp 1-2 (2004)

   D.J. Lee and I.C.F. Ipsen:   Zone Determinant Expansions for Nuclear Lattice Simulations
Phys. Rev. C, vol. 68, pp 064003 (2003)

   I.C.F. Ipsen:   A Note on Unifying Absolute and Relative Perturbation Bounds
Linear Algebra Appl., vol. 358, no. 1-3, pp 239-53 (2003)

   C. Beattie and I.C.F. Ipsen:   Inclusion Regions for Matrix Eigenvalues
Linear Algebra Appl., vol. 358, no. 1-3, pp 281-91 (2003)

   I.C.F. Ipsen:   Ritz Value Bounds that Exploit Quasi-Sparsity (2003)

   I.C.F. Ipsen:   Departure from Normality and Eigenvalue Perturbation Bounds (2003)

   I.C.F. Ipsen:   A Note on Preconditioning Non-Symmetric Matrices
SIAM J. Sci. Comput., vol. 23, no. 3, pp 1050-1 (2001)

   I.C.F. Ipsen:   An Overview of Relative sin(Theta) Theorems for Invariant Subspaces of Complex Matrices
J. Comput. Appl. Math., vol. 123, no. 1-2, pp 131-53 (2000)

   I.C.F. Ipsen:   Absolute and Relative Perturbation Bounds for Invariant Subspaces of Matrices
Linear Algebra Appl., vol. 309, no. 1-3, pp 45-56 (2000)

   I.C.F. Ipsen:   Expressions and Bounds for the Residual in GMRES
BIT, vol. 40, no. 3, pp 524-33 (2000)

   J.M. Banoczi, N.-C. Chiu, G.E. Cho, and I.C.F. Ipsen:
The Lack of Influence of the Right-Hand Side on the Accuracy of Linear System Solution
SIAM J. Sci. Comput., vol. 20, no.1, pp 203-27 (1999)

   I.C.F. Ipsen:   Relative Perturbation Bounds for Matrix Eigenvalues and Singular Values
in: Acta Numerica 1998, vol. 7, Cambridge University Press, Cambridge, pp 151-201 (1998)

   S.C. Eisenstat and I.C.F. Ipsen:   Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
SIAM J. Matrix Anal. Appl., vol. 20, no. 1, pp 149-58 (1998)

   S.C. Eisenstat and I.C.F. Ipsen:   Relative Perturbation Results for Eigenvalues and Eigenvectors of Diagonalisable Matrices
BIT, vol 38, no. 3 pp 502-9 (1998)

   I.C.F. Ipsen:   A Different Approach to Bounding the Minimal Residual Norm in Krylov Methods (1998)

   I.C.F. Ipsen and C.D. Meyer:   The Idea Behind Krylov Methods
Amer. Math. Monthly, vol. 105, no. 10, pp 889-99 (1998)

   I.C.F. Ipsen:   A Note on the Field of Values of a Non-Normal Matrix (1998)

   G.E. Cho and I.C.F. Ipsen:   If a Matrix Has Only a Single Eigenvalue, How Sensitive Is This Eigenvalue? II (1998)

   I.C.F. Ipsen:  Computing an Eigenvector with Inverse Iteration
SIAM Review, vol. 39, no. 2, pp 254-91 (1997)

   G.E. Cho and I.C.F. Ipsen:   If a Matrix Has Only a Single Eigenvalue, How Sensitive Is This Eigenvalue? (1997)

   I.C.F. Ipsen:   Helmut Wielandt's Contribution to the Numerical Solution of Complex Eigenvalue Problems
in: Helmut Wielandt, Mathematische Werke, Mathematical Works, Vol. 2: Linear Algebra and Analysis
B. Huppert and H. Schneider, eds., Walter de Gruyter, Berlin, pp 453-63 (1996)

   I.C.F. Ipsen:   A History of Inverse Iteration
in: Helmut Wielandt, Mathematische Werke, Mathematical Works, Vol. 2: Linear Algebra and Analysis
B. Huppert and H. Schneider, eds., Walter de Gruyter, Berlin, pp 464-72 (1996)

   S.L. Campbell, I.C.F. Ipsen, C.T. Kelley and C.D. Meyer:  GMRES and the Minimal Polynomial
BIT, vol. 36, no. 4, pp 664-75 (1996)

   S.C. Eisenstat and I.C.F. Ipsen:   Relative Perturbation Techniques for Singular Value Problems
SIAM J. Numer. Anal., vol. 32, no. 6, pp 1972-88 (1995)

   I.C.F. Ipsen and C.D. Meyer:   The Angle Between Complementary Subspaces
Amer. Math. Monthly, vol. 102, no. 10, pp 904-11 (1995)

   I.C.F. Ipsen and C.D. Meyer:   Uniform Stability of Markov Chains
SIAM J. Matrix Anal. Appl., vol. 15, no. 4, pp 1061-74 (1994)

   S.C. Eisenstat and I.C.F. Ipsen:   Relative Perturbation Bounds for Eigenspace Singular Vector Subspaces
in: Applied Linear Algebra, SIAM, Philadelphia, pp 62-5 (1994)

   S. Chandrasekaran and I.C.F. Ipsen:   On the Singular Value Decomposition of Triangular Matrices
in: Numerical Linear Algebra, China Science and Technology Press, Jiang Er-xiong, ed., pp 85-9 (1994)