<i>Toeplitz Forms and Their Applications</i>

Abstract. There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

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“…It is enough to prove the case n = 6 in equation (2.70) Since the proofs of the remaining cases are similar. Upon noting that 7 .…”

Section: Sinc-galerkin Methods For Solving Sixth-order Bvp 1331mentioning

confidence: 99%

“…Note that the matrices I (2) , I (4) and I (6) are m × m symmetric matrices and the matrices I (1) , I (3) and I (5) are m × m skew-symmetric matrices [7]. The matrix I (0) is the m × m identity matrix.…”

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confidence: 99%

Sinc-Galerkin method for solving linear sixth-order boundary-value problems

2003

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“…This scheme generalizes the one used by Wojtaszczyk in [28]. Both schemes are based on the orthogonal Haar-type matrices, used firstly by Olevskii to construct orthogonal systems (see [5], p. 120, [16], [17]). For the proofs of these results we refer the reader to [3] …”

Section: Construction Of Quasi-greedy Basesmentioning

confidence: 99%

Quasi-greedy Bases and Lebesgue-type Inequalities

Temlyakov¹

2015

Advanced Courses in Mathematics - CRM Barcelona

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We study Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases. We mostly concentrate on this study in the L p spaces. The novelty of the paper is in obtaining better Lebesgue-type inequalities under extra assumptions on a quasigreedy basis than known Lebesgue-type inequalities for quasi-greedy bases. We consider uniformly bounded quasi-greedy bases of L p , 1 < p < ∞, and prove that for such bases an extra multiplier in the Lebesgue-type inequality can be taken as C(p) ln(m + 1). The known magnitude of the corresponding multiplier for general (no assumption of uniform boundedness) quasi-greedy bases is of order m | 1 2 − 1 p | , p = 2. For uniformly bounded orthonormal quasi-greedy bases we get further improvements replacing ln(m + 1) by (ln(m + 1)) 1/2 .

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“…The asymptotics of polynomials orthogonal on a compact set contain a wealth of spectral information on the spectrum and the spectral measures of the polynomials. For example, under certain conditions, see Freud [24], Nevai [38], Szego [50], Grenander and Szego [26], a polynomial system {5"(x)} orthonormal on [-1, 1] will have the asymptotic development…”

Section: Ismail and Wilson [32] Established The Generating Functionmentioning

confidence: 99%