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- W2261304328 abstract "When the heat equation and wave equation are approximated by ut = −Ku and utt = −Ku (discrete in space), the solution operators involve e −Kt , √ K ,c os( √ Kt), and sinc( √ Kt). We compute these four matrices and find accurate approximations with a va- riety of boundary conditions. The second difference matrix K is Toeplitz (shift-invariant) for Dirichlet boundary conditions, but we show why eKt also has a Hankel (anti-shift- invariant) part. Any symmetric choice of the four corner entries of K leads to Toeplitz plus Hankel in all functions f (K). Overall, this article is based on diagonalizing symmetric matrices, replacing sums by integrals, and computing Fourier coefficients." @default.
- W2261304328 created "2016-06-24" @default.
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- W2261304328 date "2014-08-01" @default.
- W2261304328 modified "2023-09-27" @default.
- W2261304328 title "Functions of Difference Matrices Are Toeplitz Plus Hankel" @default.
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