An orthogonal basis for non-uniform algebraic-trigonometric spline space-中国期刊网

摘要 Non-uniformalgebraic-trigonometricB-splinessharesmostofthepropertiesasthoseoftheusualpolynomialB-splines.Buttheyarenotorthogonal.Weconstructanorthogonalbasisforthen-order(n≥3)algebraic-trigonometricsplinespaceinordertoresolvethetheoreticalproblemthatthereisnotanexplicitorthogonalbasisinthespacebynow.MotivatedbytheLegendrepolynomials,wepresentanovelapproachtodefineasetofauxiliaryfunctions,whichhavesimpleandexplicitexpressions.Thentheproposedorthogonalsplinesaregivenasthederivativesoftheseauxiliaryfunctions.

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An orthogonal basis for non-uniform algebraic-trigonometric spline space

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An orthogonal basis for non-uniform algebraic-trigonometric spline space

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