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Cited by 62 publications
(20 citation statements)
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“…is symmetric positive definite, the matrix A is almost positive definite provided that D The following lemma, originally proved in [20,28] and recently re-stated in [6], describes the eigenvalue distributions of the Toeplitz matrices T (i) (i = 1, 2, 3); see also [27]. The results follow directly from the fact that the generating functions of T (1) , T (2) and T (3) are ıθ, θ 2 and ıθ 3 , respectively.…”
Section: A Combination Of Sinc-collocation and Sinc-galerkin Methodsmentioning
confidence: 99%
“…is symmetric positive definite, the matrix A is almost positive definite provided that D The following lemma, originally proved in [20,28] and recently re-stated in [6], describes the eigenvalue distributions of the Toeplitz matrices T (i) (i = 1, 2, 3); see also [27]. The results follow directly from the fact that the generating functions of T (1) , T (2) and T (3) are ıθ, θ 2 and ıθ 3 , respectively.…”
Section: A Combination Of Sinc-collocation and Sinc-galerkin Methodsmentioning
confidence: 99%
“…The approximation of the last five inner products on the right-hand side of (2.9) has been thoroughly treated in [12]. We will list them for convenience…”
Section: Theorem 22 If There Exist Positive Constants α β and C Sumentioning
confidence: 99%
“…The remaining inner product approximations are listed in the following theorem which extends Theorem 3.1 in [12]. .18) and (2.19), respectively, we have the following bounds:…”
mentioning
confidence: 99%
“…The functions at(z), l = 0, 1,2, 3, 4 are given by F_rther detaiisconcerningthe derivationof_hesystem(3;16)and _ thoroughBpectral analysisof the component matrices can be found in [13].…”
Section: Rl(_e_ro)mentioning
confidence: 99%