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Short note on the mass matrix for Gauss-Lobatto grid points. (English) Zbl 1352.65578

Summary: The mass matrix for Gauss-Lobatto grid points is usually approximated by Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix and its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in \(O(N)\) operations instead of \(O(N^2)\).

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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