C. Boutsikas, P. Drineas and I.C.F. Ipsen:
Small Singular Values Can Increase in Lower Precision
submitted
arXiv:2303.03547
C. Boutsikas, P. Drineas and I.C.F. Ipsen:
Small Singular Values Can Increase in Lower Precision
submitted
arXiv:2303.03547
T.W. Reid, I.C.F. Ipsen, J. Cockayne, and C.J. Oates:
Statistical properties of the probabilistic numeric solver BayesCG
Numer. Math., to appear
arXiv:2208.03885
K.J. Pearce, I.C.F. Ipsen, M.A. Haider, A.K. Saibaba
and R.C. Smith:
Robust Parameter Sensitivity Analysis via Column Subset Selection
submitted
arXiv:2205.04203
E. Hallman, I.C.F. Ipsen and A.K. Saibaba:
Monte Carlo Methods for Estimating the Diagonal of a Symmetric Matrix
SIAM J. Matrix Anal. Appl., vol. 22, no. 1, pp 240-269 (2023)
arXiv:2202.02887
E. Hallman and I.C.F. Ipsen:
Precision-aware Deterministic and Probabilistic Error Bounds for
Floating Point Summation
Numer. Math., vol. 155, pp 83-119 (2023)
arXiv:2203.15928
J.T. Chi, I.C.F. Ipsen, T.-H. Hsiao, C.-H. Lin,
L.-S. Wang, W.-P. Lee, T.-P. Lu, and J.-Y. Tzeng:
SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-based
GxE Tests in Biobank Data,
(Supplement)
Frontiers in Genetics vol. 12, pp 1878 (2021)
arXiv:2105.03228
Software on github
J. Cockayne, I.C.F. Ipsen, J. Cockayne, C.J. Oates and
T.W. Reid:
Probabilistic Iterative Methods for Linear Systems
J. Mach. Learn. Res., vol. 22 (232), pp 1-34 (2021)
arXiv:2012.12615
T.W. Reid, I.C.F. Ipsen, J. Cockayne, and C.J. Oates:
BayesCG as an uncertainty aware version of CG
submitted
arXiv:2008.03225
Supplement
J.T. Chi and I.C.F. Ipsen:
A Projector-Based Approach to Quantifying Total and Excess
Uncertainties for Sketched Linear Regression
Inf. Inference, vol. 11, no. 3, pp 1055-1077 (2021)
arXiv:1808.05924
J.T. Chi and I.C.F. Ipsen:
Multiplicative Perturbation Bounds for Multivariate Multiple Linear Regression in Schatten p-Norms
Linear Algebra Appl. vol. 624, pp 87--102 (2021)
arXiv:2007.06099
I.C.F. Ipsen, and H. Zhou:
Probabilistic Error Analysis for Inner Products
SIAM J. Matrix Anal. Appl., vol. 41, no. 4, pp 1726--1741 (2020)
arXiv:1906.10465
J. Cockayne, C.J. Oates, I.C.F. Ipsen, and M. Girolami:
A Bayesian Conjugate Gradient Method (with Discussion)
(Supplement)
Bayesian Anal., vol. 14, no. 3, pp 937-1012 (2019)
arXiv:1810.03398
BA Webinar
S. Bartels, J. Cockayne, I.C.F. Ipsen
and P. Hennig:
Probabilistic Linear Solvers: A Unifying View
Stat. Comput., vol. 29, number 6, pp 1249-1263 (2019)
arXiv:1810.03398
P. Drineas and I.C.F. Ipsen:
Low-Rank Approximations Do Not Need a Singular Value Gap
SIAM J. Matrix Anal. Appl., vol. 40, no. 1, pp 299-319 (2019)
D. Frame, R. He, I.C.F. Ipsen, D.D. Lee, D.J. Lee, and
E. Rrapaj:
Eigenvector Continuation with Subspace Learning
Phys. Rev. Lett., vol. 121, no. 3, pp 032501 (2018)
Featured in Physics: Making Quantum Calculations Behave
NC State News:
Following the Path: Making Huge Calculations Predictable
Michigan State, National Superconducting Cyclotron Laboratory:
Chasing down eigenvectors
J.T. Holodnak, I.C.F. Ipsen and R.C. Smith:
A Probabilistic Subspace Bound with Appplication to Active Subspaces
SIAM J. Matrix Anal. Appl., vol. 39, no. 3, pp 1208-1220 (2018)
P. Drineas, I.C.F. Ipsen, E.-M. Kontopoulou and
M. Magdon-Ismail:
Structural Convergence Results for Approximation of Dominant
Subspaces from Block Krylov Spaces
SIAM J. Matrix Anal. Appl., vol. 39, no. 2, pp 567-586 (2018)
A.K. Saibaba, A. Alexanderian and I.C.F. Ipsen:
Randomized Matrix-Free Trace and Log-Determinant Estimators
Numer. Math., vol. 137, pp 353-395 (2017)
S. Gallopoulos, P. Drineas, I.C.F. Ipsen and M.W. Mahoney:
RandNLA, Pythons, and the CUR for your Data Problems: Reporting from
G2S3 in Delphi
SIAM News, vol. 49, no. 1, pp 7-8 (2016)
J.T. Holodnak, I.C.F. Ipsen and R.C. Smith:
Accuracy of Response Surfaces over Active Subspaces Computed with
Random Sampling
J. Guinness and I.C.F. Ipsen:
Efficicent Computation of Gaussian Likelihoods for Stationary Markov
Random Field Models
arXiv:1506.00138
J.T. Holodnak, I.C.F. Ipsen and T. Wentworth:
Conditioning of Leverage Scores and Computation by QR
Decomposition
SIAM J. Matrix Anal. Appl., vol. 36, no. 3, pp 1143-1163 (2015)
J. T. Holodnak and I.C.F. Ipsen:
Randomized Approximation of the Gram Matrix: Exact Computation and
Probabilistic Bounds
SIAM J. Matrix Anal. Appl., vol. 36, no. 1, pp 110-137 (2015)
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
T. Wentworth and I.C.F. Ipsen:
Kappa_SQ: A Matlab Package for Randomized
Sampling of Matrices with Orthonormal Columns
arXiv:1402.0642
I.C.F. Ipsen and T. Wentworth:
The Effect of Coherence on Sampling from Matrices with Orthonormal
Columns, and Preconditioned Least Squares Problems
SIAM J. Matrix Anal. Appl., vol. 35, no. 4, pp 1490-1520 (2014)
Matlab code: kappa_SQ_v3
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)