Projection Methods and the Curse of Dimensionality

Authors: Burkhard Heer, Alfred Maußner

We study the ability of three different projection methods to solve high-dimensional state space problems: Galerkin, collocation, and least squares projection. The curse of dimensionality can be reduced substantially for both Least Squares and Galerkin projection methods through the use of monomial formulas. Least Squares are shown to require a good initial value in order to give an accurate solution. Alternatively, we suggest a new ad hoc collocation method for complete polynomials that is fast and easy to implement.


Journal: Journal of Mathematical Finance
DOI: 10.4236/jmf.2018.82021 (PDF)
Paper Id: 84373 (metadata)

See also: Comments to Paper

About scirp

(SCIRP: is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in JMF. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *