APPROXIMATION OF PHYSICAL MEASUREMENT DATA BY DISCRETE ORTHOGONAL EIGENFUNCTIONS OF LINEAR DIFFERENTIAL OPERATORS
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In: Transactions of the Canadian Society for Mechanical Engineering, CSME = Transactions de la Société Canadienne de Génie Mécanique, Vol. 41.2017, No. 5, 2017, p. 804-824.
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TY - JOUR
T1 - APPROXIMATION OF PHYSICAL MEASUREMENT DATA BY DISCRETE ORTHOGONAL EIGENFUNCTIONS OF LINEAR DIFFERENTIAL OPERATORS
AU - Harker, Matthew
AU - O'Leary, Paul
PY - 2017
Y1 - 2017
N2 - We present a new method for computing the eigenfunctions of a linear differential operator such that they satisfy a discrete orthogonality constraint, and can thereby be used to efficiently approximate physical measurement data. Classic eigenfunctions, such as those of Sturm-Liouville problems, are typically used for approximating continuous functions, but are cumbersome for approximating discrete data. We take a matrix-based variational approach to compute eigenfunctions based on physical problems which can be used in the same manner as the DCT or DFT. The approach uses sparse matrix methods, so it can be used to compute a small number of eigenfunctions. The method is verified on common eigenvalue problems, and the approximation of real-world measurement data of a bending beam by means of its computed mode-shapes.
AB - We present a new method for computing the eigenfunctions of a linear differential operator such that they satisfy a discrete orthogonality constraint, and can thereby be used to efficiently approximate physical measurement data. Classic eigenfunctions, such as those of Sturm-Liouville problems, are typically used for approximating continuous functions, but are cumbersome for approximating discrete data. We take a matrix-based variational approach to compute eigenfunctions based on physical problems which can be used in the same manner as the DCT or DFT. The approach uses sparse matrix methods, so it can be used to compute a small number of eigenfunctions. The method is verified on common eigenvalue problems, and the approximation of real-world measurement data of a bending beam by means of its computed mode-shapes.
KW - eigenfunctions
KW - discrete orthogonality
KW - approximation of measurement data
U2 - 10.1139/tcsme-2017-513
DO - 10.1139/tcsme-2017-513
M3 - Article
VL - 41.2017
SP - 804
EP - 824
JO - Transactions of the Canadian Society for Mechanical Engineering, CSME = Transactions de la Société Canadienne de Génie Mécanique
JF - Transactions of the Canadian Society for Mechanical Engineering, CSME = Transactions de la Société Canadienne de Génie Mécanique
SN - 0315-8977
IS - 5
ER -
