Dr. Robert Lopez

Puttin’ on the Ritz

In this webinar, we will look at the Rayleigh quotient for finding eigenvalues of symmetric matrices, and its relation to the Rayleigh-Ritz technique for approximating solutions of the Sturm-Liouville eigenvalue problem. The gap between optimization and approximating eigenvalues of an ODE is spanned by the bridge of the variational calculus. When approximating solutions of the Sturm-Liouville BVP, this bridge is crossed by the technique of Ritz, but not necessarily of Galerkin. 

For the Raleigh quotient, see the third edition of "Applied Linear Algebra" by Noble and Daniel. For the Rayleigh-Ritz technique, see Chapter VII in Sagan’s 1961 "Boundary and Eigenvalue Problems in Mathematical Physics," or better still, Chapter IV of "Approximate Methods of Higher Analysis" by Kantorovich and Krylov, translated (1964) by Curtis Benster. 

Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books, including Advanced Engineering Mathematics. For over two decades, Dr. Lopez has also been a visionary figure in the introduction of math technology into undergraduate education and has received numerous awards for outstanding scholarship and teaching.
Language: English
Duration: 62 Minutes
Related Terms: Ritz, Rayleigh, Sturm-liouville, Ode, Calculus, Galerkin