The discrete analogue of a differential operator and its applications

Hayotov, Abdullo R.

doi:10.1007/s10986-014-9244-x

Cited by 14 publications

(13 citation statements)

References 11 publications

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“…where Remark . From Theorem 4.1, when m = 2, we get Theorem 7 of [17] and Theorem 3.1 of [19], and when m = 2, ω = 1 we get Theorem 3.1 of [18].…”

Section: Computation Of Coefficients Of Interpolation Spline (14)mentioning

confidence: 95%

“…Furthermore several properties of the discrete argument function D m (hβ) were given in [16,17]. Here we give the following properties of the discrete argument function D m (hβ) which we need in our computations.…”

Section: Preliminariesmentioning

confidence: 99%

“…(0, 1) and K 2 (P 2 ) Hilbert spaces were constructed in works [8,17,18,19,31,32] by using Sobolev's method. Furthermore, the connection between interpolation spline and optimal quadrature formula in the sense of Sard in L (m) 2 (0, 1) and K 2 (P 2 ) spaces were shown in [8] and [18].…”

Section: Introduction Statement Of the Problemmentioning

confidence: 99%

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Construction of Interpolation Splines Minimizing the Semi-norm in the Space K2(Pm)

Hayotov¹

2018

J. Sib. Fed. Univ., Math. phys.

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In the present paper, using S.L. Sobolev's method, interpolation splines that minimize the expression ∫ 1 0 (φ (m) (x)+ω 2 φ (m−2) (x)) 2 dx in the space K2(Pm) are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation splines are exact for monomials 1, x, x 2 ,. .. , x m−3 and for trigonometric functions sin ωx and cos ωx.

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“…where Remark . From Theorem 4.1, when m = 2, we get Theorem 7 of [17] and Theorem 3.1 of [19], and when m = 2, ω = 1 we get Theorem 3.1 of [18].…”

Section: Computation Of Coefficients Of Interpolation Spline (14)mentioning

confidence: 95%

Section: Preliminariesmentioning

confidence: 99%

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Construction of Interpolation Splines Minimizing the Semi-norm in the Space K2(Pm)

Hayotov¹

2018

J. Sib. Fed. Univ., Math. phys.

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“…In connection with this, the discrete analogue D m ðhmÞ of the differential operator d 2m dx 2m þ 2x 2 d 2mÀ2 dx 2mÀ2 þ x 4 d 2mÀ4 dx 2mÀ4 , which satisfies (4.11) was constructed in [12] and some properties were investigated.…”

Section: ð4:9þmentioning

confidence: 99%

Optimal quadratures in the sense of Sard in a Hilbert space

Hayotov

Milovanović

Shadimetov

2015

Applied Mathematics and Computation

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“…which satisfies (4.4) was constructed in [11] and some properties were investigated. Following [11] we have:…”

Section: Coefficients Of the Optimal Quadrature Formulamentioning

confidence: 99%

Optimal quadrature formula in the sense of Sard in K2(P3) space

Hayotov

Milovanović

Shadimetov

2014

Publ Inst Math (Belgr)

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We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K 2 (P 3). Using Sobolev's method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space L (3) 2 (0, 1). The obtained optimal quadrature formula is exact for the trigonometric functions sin x, cos x and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

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The discrete analogue of a differential operator and its applications

Cited by 14 publications

References 11 publications

Construction of Interpolation Splines Minimizing the Semi-norm in the Space K2(Pm)

Construction of Interpolation Splines Minimizing the Semi-norm in the Space K2(Pm)

Optimal quadratures in the sense of Sard in a Hilbert space

Optimal quadrature formula in the sense of Sard in K2(P3) space

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