On eigenvalues of a matrix arising in energy-preserving/dissipative continuous-stage Runge-Kutta methods
In this short note, we define an s × s matrix Ks constructed from the Hilbert matrix Hs=(1i+j-1)i,j=1s{H_s} = \left( {{1 \over {i + j - 1}}} \right)_{i,j = 1}^s and prove that it has at least one pair of complex eigenvalues when s ≥ 2. Ks is a matrix related to the AVF collocation method, which is a...
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-08-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2021-0101 |