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This page was last updated  09/20/07 11:09 PM

Ricardo D. Fierro                                      
Professor
Department of Mathematics, CSUSM

Ph.D., Mathematics, University of California, San Diego
B.S., Mathematics, University of California, Davis

Special teaching interest: mathematics for K-8 teachers

Office: 317 Science Hall 2 Phone: 760-750-4158 Fax: 760-750-3439 Email: fierro@csusm.edu Address:     Department of Mathematics             California State University San Marcos          San Marcos, CA 92096-0001 U.S.A.

Fierro Family

Courses for Fall 2007: 
Math 210 Mathematics for K-8 Teaching, I (MW 8:30am-9:45am)
Math 242 Intro to Probability and Statistics (MW 10:00am-11:15am)
Math 210 Mathematics for K-8 Teaching, I (MW 4pm-5:15pm)

Office hours: MW 11:15am-12:15pm

Current price of one gallon of gasoline (updated daily)

I think there is a world market for maybe five computers.
--T. Watson, chairman of IBM, 1944

There is no reason why anyone would want a computer in their home.
--K. Olson, founder and president of Digital Equipment Corp. in 1977

I don't think `Star Wars' can have the lasting or controversial interest of `2001: A Space Odyssey.
--D. Elliot, movie critic for the Chicago Daily News, 1977

You are a rude, thoughtless little pig.
--Alec Baldwin, 2007

It isn't about finding yourself. It's about creating yourself.
--Anonymous

Some  research:

• R.D. Fierro and P.C. Hansen, UTV Expansion Pack: Special-Purpose Rank-Revealing Algorithms. Numerical Algorithms, 40:47-66, 2005.
• R.D. Fierro and E. P. Jiang, Lanczos and the Riemannian SVD in Information Retrieval Applications, Numerical Linear Algebra with Applications, 12:355-372, 2005
• R.D. Fierro, Lanczos, Householder transformations, and deflation for fast and reliable subspace computation, Numerical Linear Algebra with Applications, 8:245-264, 2001.
• R.D. Fierro and M. W. Berry, Efficient computation of the Riemannian SVD in total least squares problems in information retrieval, in S. Van Huffel and P. Lemmerling (Eds.), Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms, and Applications, Kluwer Academic Publishers, 2002, pp. 349-360.
• R.D. Fierro and P.C. Hansen, Truncated VSV solutions to symmetric rank-deficient problems, B.I.T., 42:531-540, 2002.
• R.D. Fierro, P.C. Hansen, and P.S. Hansen, UTV Tools: Matlab templates for rank revealing UTV decompositions, Numerical Algorithms, 20:165-194, 1999.
• M.W. Berry and R.D. Fierro, Low-rank orthogonal decompositions for information retrieval applications, Numerical Linear Algebra with Applications, 3: 301-327, 1996.
• J.R. Bunch and R.D. Fierro, A constant false alarm rate algorithm, Linear Algebra and Its Applications, 172: 231-241, 1992.
• R.D. Fierro, Perturbation theory for two-sided (or complete) orthogonal decompositions, SIAM J. Matrix Analysis and Applications, 17:383-400, 1996.
• R.D. Fierro and J.R. Bunch, Bounding the subspaces obtained by rank revealing two-sided orthogonal decompositions, SIAM J. Matrix Analysis and Applications, 3:743-759, 1995.
• R.D. Fierro and J.R. Bunch, Collinearity and total least squares, SIAM J. Matrix Analysis and Applications, 15:1167-1181, 1994.
• R.D. Fierro and J.R. Bunch, Orthogonal projection and total least squares, Numerical Linear Algebra with Applications, 2:135-153, 1995.
• R.D. Fierro and J.R. Bunch, Perturbation theory for orthogonal projection methods with applications to least squares and total least squares, Linear Algebra and Its Applications, 234:71-96, 1996.
• R.D. Fierro, G.H. Golub, P.C. Hansen, and D. O'Leary, Regularization by total least squares, SIAM J. Scientific Computing, 18:1223-1241, 1997.
• R.D. Fierro and P.C. Hansen, Accuracy of TSVD solutions computed from rank revealing decompositions, Numerische Mathematik, 70:453-471, 1995.
• R.D. Fierro and P.C. Hansen, Recent developments in rank revealing and Lanczos methods for solving TLS-related problems, in S. Van Huffel and P. Lemmerling (Eds.), Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms, and Applications, Kluwer Academic Publishers, 2002, pp. 47-56.
• R.D. Fierro, L. Vanhamme, and S. Van Huffel, Total least squares algorithms based on rank-revealing orthogonal decompositions, in S. Van Huffel (Ed.), Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, SIAM Publications, Philadelphia, 99-116, 1996.
• L. Vanhamme, R.D. Fierro, S. Van Huffel, and R. de Beer, Fast removal of residual water in proton spectra, Journal of Magnetic Resonance, 132:197-203, 1998.

Software packages:

• R.D. Fierro, P.C. Hansen, and P.S. Hansen, UTV Tools: Matlab templates for rank revealing UTV decompositions, 1999. Available at http://www.netlib.org/numeralgo or below.

• R.D. Fierro and P.C. Hansen, UTV Expansion Pack: Special-Purpose Rank-Revealing Algorithms, 2005.

Rank-revealing decompositions are used in signal processing and many other applications where efficient and reliable updating and downdating algorithms are required, and where the reliable computation and tracking of the numerical rank of a matrix is crucial. The Matlab package UTV Tools provides 46 Matlab functions and 8 demonstration script files for computing and modifying rank-revealing URV and ULV decompositions (collectively known as UTV decompositions), including routines for RRQR decompositions, plus a 97-page User's Guide. The software can be used as is, or can be considered as templates for specialized implementations on signal processors and similar dedicated hardware platforms. The package and a survey of the underlying theory is published in the journal Numerical Algorithms (see above), but is also available below.



   Brief overview of the m-files in UTV Tools
   The User's Guide discusses the underlying theory and algorithms
   The User's Guide  plus the Matlab routines in UTV Tools are also available

 

Accurate and efficient quantification of magnetic resonance spectroscopy signals is important in medical diagnosis. In particular, the quantification of signals due to metabolites is important because it is related to the concentration of metabolites, which has important interpretations to the biomedical community. The measured signal mainly contains contributions due to both water and metabolites of interest. The water contribution dominates the measured signal and this "noise" must be removed before accurate quantification of the signal due to metabolites can be done. It turns out in these applications the water contributions can be modeled by a sum of damped exponentials. A new iterative algorithm (TKSVD) written in the Matlab programming language can be used for determining the corresponding parameters (frequencies, damping factors, amplitutes, and phase shifts). TKSVD is a Lanczos-based method that takes into account the structure in the problem and uses reorthogonalization and explicit restarts. Our numerical results below concerning the CPU time and computational demand for modeling the intense water peak of an MRS brain signal   illustrate that TKSVD can be used as a front-end in these biomedical applications for removing water contributions that can be modeled as a sum of damped exponentials. This work is inspired by the many publications by Leen Vanhamme and Sabine Van Huffel (Department of Engineering, K.U., Leuven, Belgium) in the area of accurate and efficient quantification of magnetic resonance spectroscopy signals. This work is joint work with Per Christian Hansen, Informatics and Mathematical Modeling, Technical University of Denmark (Lyngby, Denmark). A brief description of   TKSVD can be found in "R.D. Fierro and P.C. Hansen, Recent developments in rank revealing and Lanczos methods for solving TLS-related problems, in S. Van Huffel and P. Lemmerling (Eds.), Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms, and Applications, Kluwer Academic Publishers, 2002, pp. 47-56."

Below are results of some experiments based on Data Set 002 from the BioSource Database (http://www.esat.kuleuven.ac.be/sista/members/biomed/data002.htm) which consists of voxels that are part of an image of a human brain. The analysis of Nuclear Magnetic Resonance (NMR) data is very difficult and requires expertise in NMR spectroscopy to determine the chemical properties of the physical matter. Therefore, we provide numerical results without regard to its relation to chemical properties. All computations were performed with Matlab on a PC with a Pentium III 450 MHz processor and 128 MB of memory. For typical data in this database, the first few singular values of the m-by-n data matrix composed of N signal samples decay rapidly, but the remaining singular values decay slowly, making them more "difficult" to capture. The results of TKSD depend on the starting vector, among other confounding parameters, and the particular data set. Therefore, for each signal, we report large-sample 95% confidence intervals for the expected flop count and CPU time (seconds) using 100 samples, where TKSVD used a random starting vector each time. In all the samples we chose N = 1024, m = 513, n = 512, orders k = 15 and 30, accuracy tolerance 0.00001, and the maximum number of Lanczos iterations 2k.

To compare the numerical results, we carefully implemented a Matlab routine for  bidiagonalizing a 513-by-512 complex Toeplitz matrix (N = 1024) using Householder transformations and accumulating only the right transformations. This approach, which represents the first phase of a specialized SVD algorithm for subspace computation, required 2830 Mega-floating point operations and 384.97 seconds, while Matlab's "economy size" built-in SVD routine required 5780 Mega- floating point operations and 139.68 seconds.

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page last updated: 09/20/07