James Baglama


Dr. James Baglama Chair of Mathematics
Department of Mathematics
University of Rhode Island
Kingston, Rhode Island 02881
Office: Lippitt Hall 202H
Phone: 401.874.2709
Fax: 401.874.4454


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Spring 2014 Math 111 Software Calc-Bowl 2014
Summer 2014 Math 111 Summer 2014 Math 108 AAUP



Education


Professional Links


Software


EIGENVALUES
Symmetric
The program irbleigs.m is a MATLAB program for computing a few eigenvalues and associated eigenvectors located anywhere in spectrum of a large sparse Hermitian matrix. The irbleigs.m program is matrix-free, i.e., the matrix is accessed only through the evaluation of matrix-vector products. In particular the factorization of A is not demanded, nor is the solution of linear systems of equations with the matrix A. The code can also compute the generalized eigenpairs of certain generalized eigenvalue problems. A MATLAB GUI demo irbldemo.m is an easy to use interface with irbleigs.m that allows the user to quickly change the parameter options in irbleigs.m. This helps illustrates the different choices for the parameters available in irbleigs.m.
Click here to download the MATLAB code irbleigs.m.
Click here to download the MATLAB GUI demo irbldemo.m.
Non-Symmetric
The program ahbeigs.m is a MATLAB program for computing a few eigenvalues and associated eigenvectors located anywhere in spectrum of a large sparse non-symmetric matrix. The program ahbeigs.m is based on a block Arnoldi method that makes use of Householder reflections to maintain orthogonality and restarting is accomplished by augmentation of the Krylov subspace with Schur vectors. No factorization is required in order to find extreme eigenvalues, however factorization is performed when searching for non-extreme eigenvalues. The program can solve the standard or the generalized eigenvalue problem. Research supported by NSF grant DMS-0311786.
Click here to download the MATLAB code ahbeigs.m.


SINGULAR VALUES
The routine irblsvds.m is a MATLAB program for computing a few singular values and singular vectors of a m x n matrix A. irblsvds.m uses the (m+n) x (m+n) Hermitian matrix Z = [0 A; A' 0] and calls irbleigs.m to find a few eigenvalues and eigenvectors of the matrix Z. The singular values of A are the positive eigenvalues of Z, the "right" singular vectors V, correspond to the last n elements of the eigenvectors of Z, and the "left" singular vectors U, correspond to the first m elements of the eigenvectors of Z.
Click here to download the MATLAB code irblsvds.m.
The routines irlba.m and irlbablk.m are MATLAB programs for computing a few singular values and singular vectors of a m x n matrix A. irlba.m is a restarted Lanczos bidiagonalization method and irlbablk.m is a restarted block Lanczos bidiagonalization method. Restarting is carried out by augmentation of Krylov subspaces with either Ritz vectors or harmonic Ritz vectors.
Click here to download the MATLAB code irlba.m.
Click here to download the block MATLAB code irlbablk.m.
Click here to download the matrix hypatia.gz.
 
The code irlba has also been written in the language R by Bryan Lewis. Click here for the video and slides.
Click here for the R verison of the code irlba. Code is maintained by Bryan Lewis.
Click here for the R package on CRAN for the code irlba. Code is maintained by Bryan Lewis.


LEAST SQUARES
The routines alsqr.m and irlsqr.m are MATLAB programs for computing the solution of min ||Ax-b|| where A is an (m x n) matrix, b an (m x 1) vector, and x is an (n x 1) vector. b is not assumed to be in span(Col(A)). The routine alsqr.m is an augmented preconditioned LSQR method. The preconditioner is computed via an augmented Lanczos bidiagonalization method with harmonic Ritz vectors. The program then runs LSQR on the preconditioned system. The routine irlsqr.m is a preconditioned implictly restarted LSQR method, that is mathematically equivalent to< i>alsqr.m . The preconditioner is computed via implicitly restarted Lanczos bidiagonalization method with harmonic Ritz values. The program then runs LSQR on the preconditioned system.
Click here to download the MATLAB code alsqr.m.
Click here to download the MATLAB code irlsqr.m.



Papers
  1. Iterative Methods for the Computation of a Few Eigenvalues of a Large Symmetric Matrix
    (with D.Calvetti and L.Reichel), BIT, 36 (1996), pp. 400-421.
    paper1.pdf
       
  2. Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling
    (with D. Calvetti, L. Reichel, and A. Ruttan) Journal of Computational Physics, 146, (1998) pp. 203-226.
    paper2.pdf
       
  3. Fast Leja points
    (with D.Calvetti and L.Reichel) ETNA (1998) Vol. 7, (1998) pp. 126-140.
    paper3.pdf
       
  4. Adaptively Preconditioned GMRES Algorithms
    (with D. Calvetti, G.H. Golub, and L. Reichel) ,SIAM J. Sci. Comput., 20, No. 1, (1998), pp. 243-269.
    paper4.pdf
       
  5. Qualitative behavior of a variable-yield simple food chain with an inhibiting nutrient
    (with S. R. Jang), Mathematical Biosciences, 164, (2000) pp. 65-80.
    paper5.pdf
       
  6. Numerical Approximation of the Product of the Square Root of a Matrix With a Vector
    (with E. J. Allen and S. K. Boyd) Linear Algebra and Its Applications, 310, (2000) pp. 167-181.
    paper6.pdf
       
  7. Dealing With Linear Dependence during the Iterations of the Restarted Block Lanczos Methods
    Numerical Algorithms, 25, (2000) pp. 23-36.
    paper7.pdf
       
  8. A nutrient-prey-predator model with intratrophic predation
    (with S. R. Jang), Applied Mathematics and Computation, 129, (2002), pp. 517-536.
    paper8.pdf
       
  9. IRBL: An Implicitly Restarted Block Lanczos Method for Large-Scale Hermitian Eigenproblems
    (with D.Calvetti and L.Reichel) SIAM J. Sci. Comput., 24, No. 5, (2003), pp. 1650-1677.
    paper9.pdf
       
  10. irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix
    (with D.Calvetti and L.Reichel) TOMS, Vol. 29, No. 5, (2003), pp. 337-348.
    paper10.pdf
       
  11. Persistence in variable-yield nutrient-plankton models with nutrient recycling
    (with S. R. Jang), Mathematical and Computer Modelling, 38 (2003), pp. 281-298.
    paper11.pdf
       
  12. Intratrophic predation in a simple food chain with fluctuating nutrient
    (with S. R. Jang and P. Seshaiyer), Discrete and Continuous Dynamical Systems-Series B, Vol. 5, No. 2, May (2005), pp. 335-352.
    paper12.pdf
       
  13. Nutrient-plankton models with nutrient recycling
    (with S. R. Jang) Computers and Mathematics with Application, Vol. 49, (2005), pp. 375-387.
    paper13.pdf
       
  14. Augmented Implicitly Restarted Lanczos Bidiagonalization Methods
    (with L. Reichel) SIAM J. Sci. Comput., 27 (2005), pp. 19-42.
    paper14.pdf
       
  15. Droop models of nutrient-plankton interaction with intratrophic predation
    (with S. R. Jang) Applied Mathematics and Computation, Vol. 169, (2005), pp. 1106-1128.
    paper15.pdf
       
  16. Nutrient-phytoplankton-zooplankton models with a toxin
    (with S. R. Jang and J. Rick) Mathematical and Computer Modelling, Vol. 43, Issues 1-2, January (2006), pp. 105-118.
    paper16.pdf
       
  17. Restarted Block Lanczos Bidiagonalization Methods
    (with L. Reichel) Numerical Algorithms, 43 (2006), pp. 251-272.
    paper17.pdf
       
  18. Nutrient-Plankton Interaction with a Toxin in a Variable Input Nutrient Environment (with S. R. Jang) Current Development in Mathematical Biology, Proceedings of the Conference on Mathematical Biology and Dynamical Systems, Series on Knots and Everything, 38 (2007), ISBN 981-270-015-3.
    paper18.pdf
       
  19. Decomposition methods for large linear discrete ill-posed problems
    (with L. Reichel) Journal of Computation and Applied Mathematics, 18 (2007), pp. 332-343.
    paper19.pdf
       
  20. Augmented GMRES-type methods
    (with L. Reichel) Numer. Linear Algebra Appl., 14 (2007), pp. 337-350.
    paper20.pdf
       
  21. Augmented Block Householder Arnoldi Method
    Linear Algebra Appl.,Vol. 429, Issue 10, (2008) pp. 2315-2334
    paper21.pdf
       
  22. Plankton-toxin interaction with a variable input nutrient
    (with S. R. Jang and J. Rick) Journal of Biological Dynamics, Volume 2, Issue 1 (2008), pp. 14 - 30
    paper22.pdf
       
  23. Continuous-time predator-prey models with parasites
    (with S.R. Jang) Journal of Biological Dynamics, Volume 3, (2009) pp. 87 - 98
    paper23.pdf
       
  24. Random dispersal in a predator-prey-parasite system
    (with S. R. Jang and L. Wu) Journal of Biological Systems, Vol. 18, No. 4 (2010) pp. 825 - 845
    paper24.pdf
       
  25. An Implicitly Restarted Block Lanczos Bidiagonalization Method Using Leja Shifts
    (with L. Reichel) BIT Numerical Mathematics Vol. 53, Issue 2 (2013) pp 285-310
    http://link.springer.com/article/10.1007%2Fs10543-012-0409-x
       
  26. An Augmented LSQR Method
    (with L. Reichel and D. Richmond) Numerical Algorithms Volume 64, Issue 2 (2013), pp 263-293.
    http://link.springer.com/article/10.1007%2Fs11075-012-9665-8
       
  27. Dynamics of phytoplankton-zooplankton systems with toxin producing phytoplankton
    (with S. R. Jang and L. Wu) Applied Mathematics and Computation, Vol. 227, (2014) pp. 717-740.
       
  28. Implicitly Restarting the LSQR Algorithm
    (with D. Richmond) ETNA, Vol. 42 (2014) pp. 85-105.
    http://etna.mcs.kent.edu/vol.42.2014/pp85-105.dir/pp85-105.pdf
       
  29. Analysis of directed networks via partial singular value decomposition and Gauss quadrature
    (with C. Fenu, L. Reichel, and G. Rodriguez) Linear Algebra and its Applications Vol. 456 (2014) pp. 93-121
    http://www.sciencedirect.com/science/article/pii/S0024379514003097

       


Quotes


"Experience is what you get when you didn't get what you wanted"
- Randy Pausch


"Don't waste time calculating your chances of success and failure. Just fix your aim and begin"
- Guan Yin Tzu


"An invisible red thread connects those who are destined to meet, regardless of time, place, or circumstance. The thread may stretch or tangle, but will never break."
- An ancient Chinese belief


"The most exciting phrase to hear in science, the one that heralds new discoveries, is not `Eureka!' but `That's funny...' "
- Isaac Asmiov


"Time and space are modes by which we think and not conditions in which we live."
- Albert Einstein


"It is a miracle that curiosity survives formal education."
- Albert Einstein


" It is the supreme art of the teacher to awaken joy in creative expression and knowledge."
- Albert Einstein


"I am not a teacher, I am an awakener."
- Robert Frost


"If nothing's fair, why can't it ever be unfair in *my* favor?"
- Calvin and Hobbes, "Calvin and Hobbes"



NOTICE: The information presented on this page represents the personal views, ideas, and opinions of the author. This is not an official University of Rhode Island web page. Links contained at this web site to other organizations, are presented as a service and neither constitute nor imply university endorsement or warranty.


James Baglama