|Appears in Collections:||Computing Science and Mathematics Conference Papers and Proceedings|
|Title:||Sparse interpolation and rational approximation|
|Citation:||Cuyt A & Lee W (2016) Sparse interpolation and rational approximation. In: Hardin D, Lubinsky D & Simanek B (eds.) Modern Trends in Constructive Function Theory. Contemporary Mathematics, 661. Constructive Functions 2014 - Conference in Honor of Ed Saff's 70th Birthday, Nashville, TN, USA, 26.05.2014-30.05.2014. Providence, RI, USA, pp. 229-242. https://bookstore.ams.org/conm-661|
|Series/Report no.:||Contemporary Mathematics, 661|
|Conference Name:||Constructive Functions 2014 - Conference in Honor of Ed Saff's 70th Birthday|
|Conference Dates:||2014-05-26 - 2014-05-30|
|Conference Location:||Nashville, TN, USA|
|Abstract:||Sparse interpolation or exponential analysis, is widely used and in quite different applications and areas of science and engineering. Therefore researchers are often not aware of similar studies going on in another field. The current text is written as a concise tutorial, from an approximation theorist point of view. In Section 2 we summarize the mathematics involved in exponential analysis: structured matrices, generalized eigenvalue problems, singular value decomposition. The section is written with the numerical computation of the sparse interpolant in mind. In Section 3 we outline several connections of sparse interpolation with other mostly non-numeric subjects: computer algebra, number theory, linear recurrences. Some problems are only solved using exact arithmetic. In Section 4 we connect sparse interpolation to rational approximation theory. One of the major hurdles in sparse interpolation is still the correct detection of the number of components in the model. Here we show how to reliably obtain the number of terms in a numeric and noisy environment. The new insight allows to improve on existing state-of-the-art algorithms.|
|Status:||AM - Accepted Manuscript|
|Rights:||The publisher has not responded to our queries therefore this work cannot be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.|
|SIRA.pdf||Fulltext - Accepted Version||356.97 kB||Adobe PDF||Under Permanent Embargo Request a copy|
Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependent on the depositor still being contactable at their original email address.
This item is protected by original copyright
Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
If you believe that any material held in STORRE infringes copyright, please contact email@example.com providing details and we will remove the Work from public display in STORRE and investigate your claim.