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Reducing the computational requirements of the differential quadrature method. (English) Zbl 0868.65014

It is shown that the weighting coefficient matrices of the differential quadrature method are centrosymmetric or skew centrosymmetric. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrices can reduce the computational effort for calculating the inverse, determinant, eigenvectors, and eigenvalues. Numerical results are presented which demonstrate the computational advantage.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F40 Numerical computation of determinants
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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