On an exponential-trigonometric natural interpolation spline
A.K. Boltaev, D.M. Akhmedov
Abstract
In the present paper, using the discrete analogue of the operator d8/dx8 + 2d4/dx4 + 1, an interpolation spline that minimizes the quantity ∫01(φIV(x)+φ(x))2dx in the Hilbert space W2(4,0) is constructed. Explicit formulas for the coefficients of the interpolation spline are obtained. The obtained interpolation spline is exact for the exponential-trigonometric functions e22xcos(22x),e22xsin(22x),e−22xcos(22x)and e−22xsin(22x). At the end of the paper we give some numerical results which confirm our theoretical results.
Topics & Concepts
Interpolation (computer graphics)Spline (mechanical)TrigonometrySpline interpolationTrigonometric interpolationExponential functionComputer scienceApplied mathematicsHilbert spaceMathematicsAlgorithmDiscrete mathematicsPolynomial interpolationArtificial intelligencePure mathematicsMathematical analysisBilinear interpolationComputer visionPhysicsMotion (physics)ThermodynamicsAdvanced Numerical Analysis TechniquesIterative Methods for Nonlinear EquationsMathematical functions and polynomials