Rodrigo Platte’s primary research interests are in computational mathematics, numerical analysis, and approximation theory. A recurring theme in his research is sampling. Today’s world is increasingly rich in data, but working with large data sets can be computationally expensive and, in some cases, even detrimental to the accuracy of the information being extracted. In other cases, data acquisition can be limited due to hardware restrictions or other physical constraints. Among his main contributions are the analysis and development of high-order and spectral methods, and the design of algorithms for image reconstruction from Fourier samples. His work is motivated by problems arising in medical and radar imaging, atmospheric research, terrain modeling, and fluid mechanics.
Education
Ph.D. University of Delaware 2005
Research Interests
Numerical analysis, computation mathematics
Publications
Rodrigo B. Platte, Lloyd N. Trefethen, Arno B.J. Kuijlaars. Impossibility of fast stable approximation of analytic functions from equispaced samples. SIAM Review (2011).
Rodrigo B. Platte. How fast do radial basis function interpolants of analytic functions converge?. IMA Journal of Numerical Analysis (2011).
Justin Holmer, Rodrigo B. Platte, Svetlana Roudenko. Blow-up criteria for the 3D cubic nonlinear Schrödinger equation. Nonlinearity (2010).
Ricardo Pachón, Rodrigo B. Platte, Lloyd N. Trefethen. Piecewise-smooth chebfuns. IMA Journal of Numerical Analysis (2010).
Rodrigo B. Platte, Lloyd N. Trefethen. Chebfun: a new kind of numerical computing. Progress in Industrial Mathematics at ECMI 2008. Springer (2010).
Gelb,Anne*, Platte,Rodrigo B. Developing Fast Accurate and Robust Numerical Algorithms. DOD-AFOSR(6/1/2015 - 5/31/2018).
Gelb,Anne*, Platte,Rodrigo B, Renaut,Rosemary Anne. International Conference on High Order and Spectral Methods Participant costs:2014. DOD-NAVY-ONR(6/15/2014 - 9/1/2015).
Renaut,Rosemary Anne*, Gelb,Anne, Platte,Rodrigo B. Participant expenses: International Conference on Spectral and High Order Methods 2014. DOD-AFOSR(6/1/2014 - 5/31/2015).
Kostelich,Eric John*, Armbruster,Hans Dieter, Czygrinow,Andrzej Michal, Fishel,Susanna, Gelb,Anne, Jacobs,Mark, Kawski,Matthias, Kuang,Yang, Mahalov,Alex, Moustaoui,Mohamed, Platte,Rodrigo B, Tang,Wenbo. MCTP: Mathematics Mentoring Partnership Between Arizona State University and the Maricopa County Community College District. NSF-MPS-DMS(7/15/2012 - 6/30/2017).
Gelb,Anne*, Platte,Rodrigo B, Renaut,Rosemary Anne. Development and Analysis of Non-Classical Numerical Approximation Methods. DOD-AFOSR(7/15/2012 - 7/14/2015).
Rodrigo B. Platte. Fourier reconstruction of univariate piecewise-smooth functions from non-uniform spectral data with exponential convergence rates. Research Cluster: Computational Challenges in Sparse and Redundant Representations (Nov 2014).
Rodrigo B. Platte. Impact of Waves Along Coastlines. IMA Hot Topics Workshop (Oct 2014).
Rodrigo B. Platte. Scattered data approximation and solution of PDEs on complex domains. Colloquium, Department of Mathematics, University of Arizona (Oct 2014).
Rodrigo B. Platte. Algorithms for recovering smooth functions from uniformly sampled data. International Conference on Spectral and High Order Methods (ICOSAHOM), Salt Lake City (Jun 2014).
Rodrigo B. Platte. Mini-symposium: Advances in Radial Basis Function and Other Meshfree Methods. International Conference on Spectral and High Order Methods (ICOSAHOM), Salt Lake City (Jun 2014).
Rodrigo B. Platte, Anne Gelb, Ben Adcock, Jan Hesthaven, Edward Walsh. Understanding the mathematical underpinnings in medical imaging. AIM SQuaREs, American Institute of Mathematics, Palo Alto, CA (Oct 2013).
Rodrigo B. Platte. Stability of radial basis function methods for convection problems on the circle and sphere. SIAM Annual Meeting (Jun 2013).
Rodrigo B. Platte. Computing on surfaces with Chebfun2. SIAM Annual Meeting (Jun 2013).
Rodrigo B. Platte. Mapped polynomial methods for approximation on equispaced points. Colloquium, University of Fribourg, Switzerland (May 2013).
Rodrigo B. Platte. Algorithms for approximation on equispaced nodes and the generalized Hermite error formula. Numerical Analysis Seminar, Mathematical Institute, University of Oxford (May 2013).
Rodrigo B. Platte. Algorithms for recovering smooth functions from equispaced data and the impossibility theorem. Colloquium, Boise State University (May 2013).
Rodrigo B. Platte. Algorithms for recovering smooth functions from equispaced data. Seminar, Purdue University (Apr 2013).
Rodrigo B. Platte. Algorithms for recovering smooth functions from equispaced data: from rational interpolation to compactly supported radial basis function methods. Computational and Applied Mathematics Seminar, Arizona State University (Oct 2012).
Rodrigo B. Platte. Accurate representation of Fourier transforms of piecewise smooth functions. Chebfun and Beyond Workshop, Oxford, United Kingdom (Sep 2012).
Rodrigo B. Platte. Convergence and stability properties of a family of $C^\infty$ compactly supported kernels. 3rd Dolomites Workshop on Constructive Approximation and Applications, Italy (Sep 2012).
Rodrigo B. Platte. Algorithms for recovering smooth functions from equispaced data. 3rd Dolomites Workshop on Constructive Approximation and Applications, Italy (Sep 2012).
Rodrigo B. Platte. A hybrid Fourier-polynomial method for partial differential equations. Banff International Research Station (BIRS) -- Workshop organized by Oscar Bruno (Caltech) (Jun 2012).
Rodrigo B. Platte. Algorithms for recovering smooth functions from equally spaced data. University of Delaware Colloquium (Feb 2012).
Rodrigo B. Platte. $C^\infty$ Radial Basis Function Methods for PDEs. 7th International Congress on Industrial and Applied Mathematics - ICIAM 2011 (Jul 2011).
Rodrigo B. Platte. Exploring logistic maps with Chebfun. 7th International Congress on Industrial and Applied Mathematics - ICIAM 2011 (Jul 2011).
Rodrigo B. Platte. Convergence properties of analytic and $C^\infty$ compactly-supported RBF interpolation. NSF-CBS conference on Radial Basis Functions Mathematical Developments and Applications (Jun 2011).
Rodrigo B. Platte. $C^\infty$ compactly supported radial basis function approximations. International Symposium in Approximation Theory (May 2011).
Rodrigo B. Platte. Exploring Logistic Maps with Chebfun. Computational and Applied Mathematics Seminar, Arizona State University (Nov 2010).
Rodrigo B. Platte. $C^\infty$ Compactly Supported Radial Basis Function Methods for PDEs. SIAM Annual Meeting, Pittsburgh, PA (Jul 2010).
Rodrigo B. Platte. How fast do radial basis function interpolants of analytic functions converge?. 13th International Conference on Approximation Theory, San Antonio, TX (Mar 2010).
Rodrigo B. Platte. Impossibility of approximating analytic functions from equispaced samples at geometric convergence rate. 13th International Conference on Approximation Theory, San Antonio, TX (Mar 2010).
Rodrigo B. Platte. Signal reconstruction with radial basis functions. Southwest Conference on Integrated Mathematical Methods in Medical Imaging (Feb 2010).
Rodrigo B. Platte. Impossibility of approximating analytic functions from equispaced samples at geometric convergence rates. Computational and Applied Mathematics Seminar, Arizona State University (Feb 2010).
