TY - GEN

T1 - Time-Variant System Approximation via Later-Time Samples

AU - Aceska, Roza

AU - Kim, Yeon Hyang

N1 - Funding Information:
This material is based upon work supported by the National Security Agency under Grant No. H98230-18-0144 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during Summer 2018. The authors thank the referees for their valuable comments.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - We develop a mathematical framework and efficient computational schemes to obtain an approximate solution of partial differential equations (PDEs) via sampled data. Recently, DeVore and Zuazua revisited the classical problem of inverse heat conduction, and they investigated how to recover the initial temperature distribution of a finite body from temperature measurements made at a fixed number of later times. In this paper, we consider a Laplace equation and a variable coefficient wave equation. We show that only one sensor employed at a crucial location at multiple time instances leads to a sequence of approximate solutions, which converges to the exact solution of these PDEs. This framework can be viewed as an extension of the novel, dynamical sampling techniques.

AB - We develop a mathematical framework and efficient computational schemes to obtain an approximate solution of partial differential equations (PDEs) via sampled data. Recently, DeVore and Zuazua revisited the classical problem of inverse heat conduction, and they investigated how to recover the initial temperature distribution of a finite body from temperature measurements made at a fixed number of later times. In this paper, we consider a Laplace equation and a variable coefficient wave equation. We show that only one sensor employed at a crucial location at multiple time instances leads to a sequence of approximate solutions, which converges to the exact solution of these PDEs. This framework can be viewed as an extension of the novel, dynamical sampling techniques.

KW - Dynamical system

KW - Evolutionary systems representations

KW - Initial datum

KW - Near-best approximation

UR - http://www.scopus.com/inward/record.url?scp=85101423632&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-57464-2_1

DO - 10.1007/978-3-030-57464-2_1

M3 - Conference contribution

AN - SCOPUS:85101423632

SN - 9783030574635

T3 - Springer Proceedings in Mathematics and Statistics

SP - 1

EP - 9

BT - Approximation Theory XVI, 2019

A2 - Fasshauer, Gregory E.

A2 - Neamtu, Marian

A2 - Schumaker, Larry L.

PB - Springer

Y2 - 19 May 2019 through 22 May 2019

ER -