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from Part I - Matrix Methods
Published online by Cambridge University Press: 18 February 2021
The eigenvalues and eigenfunctions of self-adjoint differential operators provide the basis functions with respect to which ordinary and partial differential equations can be solved.These methods are extensions of those used to solve linear systems of algebraic equations and ordinary differential equations.Eigenfunction expansions also provide the basis for advanced numerical methods, such as spectral methods, and data-reduction techniques, such as proper-orthogonal decomposition.
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