Professor Charles Van Loan
Department of Computer Science
5153 Upson Hall
Ithaca, NY 14850
Professor Van Loan received his undergraduate and graduate degrees in mathematics from the University of Michigan (1965-1973). He was a Research Fellow at the University of Manchester (1974-75) and has been a faculty member in the Department of Computer Science at Cornell University since 1975. His research focus is in the field of numerical linear algebra with a current emphasis on tensor computation.
He has written six textbooks: Insight Through Computing--A Matlab Introduction to
Computational Science and Engineering (with D. Fan), Matrix Computations, Third Edition (with G.H. Golub), Handbook for Matrix Computations (with T. Coleman), Computational Frameworks for the Fast Fourier Transform, Introduction to Computational Science and Mathematics, and Introduction to Scientific Computation--A Matrix/Vector Approach Using Matlab.
If Copernicus and Kepler Had Computers: An Introduction to Model-Building and Computational Science
If you watch Mars against the backdrop of the fixed stars, then night after night you'll see rather steady progress across the zodiac. But every so often, the planet appears to "back-up" before continuing on its forward trek. This periodic, retrograde motion wreaks havoc with a model of the solar system that places each planet on a steadily rotating circle with Earth at the center. Ptolemy did a pretty good job patching up the model by placing each planet on a small rotating circle whose center is on the rim of a larger rotating circle. The path traced out is called an epicycle and it offers some explanation for Mars' orbital wanderings. The epicycle model lasted for centuries until Copernicus set the record straight by suggesting that the Earth revolved around the sun along with the other planets. But would he have been so bold a scientist if he had access to 2010 computers? Or would he have just mouse-clicked his way into fame, developing a simulation package that supported further tinkering with the Ptolemaic model?
Fitting Conics to Data: A Preview of Scientific Computing
What is the smallest ellipse that can enclose n points in the plane? This is a 5-parameter optimization problem. The solution highlights the importance of approximation, heuristics, and getting the right representation.
From Chaos to Ellipse: Using Eigenvalues and Eigenvectors to Explain Phenomenon
Let P(0) be a given random polygon in the plane. Let P(k+1) be obtained from P(k) by
connecting P(k)’s side midpoints in order and then normalizing the vertex vectors x and y so that
they each have unit-2norm length . Why is it that the vertices of P(k) converge to an ellipse
having a 45-degree tilt? A simple eigenvalue/ singular value analysis explains it all.
1-2-3-Infinity: From Vector to Matrix to Tensor and Beyond
A tensor is a higher dimensional matrix. More than two subscripts are required to
identify an entry, e.g., A(i,j,k). An m-by-n-by-p tensor can be regarded as a stack of p matrices,
each m-by-n. Why do discretizations in high dimensions lead to tensors? How might they be
decomposed or combined? Why is numerical multilinear algebra the “next big thing” in scientific computing? This talk will give a snapshot of the ongoing transition from matrix-basedcomputational thinking to tensor-based computational thinking.