Abstract
In this chapter, we focus on the numerical solution of large eigenvalue problems arising in finite-rank discretizations of integral operators.
Let X be a Banach space over ℂ and T a compact linear operator defined on X. We aim to solve numerically the eigenvalue problem
with λ nonzero and ϕ defined in X. Approximations λ m and ϕ m for the spectral elements of the integral operator can be obtained by solving
where (T m ) is a sequence of finite-rank operators converging to T [AhLa01]. By evaluating the projected problem on a specific basis function, it is reduced to a matrix spectral problem
for a finite matrix A m [AhLa06].
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Vasconcelos, P.B., Marques, O., Roman, J.E. (2010). High-Performance Computing for Spectral Approximations. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 2. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4897-8_33
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DOI: https://doi.org/10.1007/978-0-8176-4897-8_33
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