Publication: Sendelenimsizlik teoreminin yaklaştırım ve sayısal integrasyona uygulanması
Abstract
Sendelenimsizlik Teoreminin Yaklaştırım ve Sayısal İntegrasyona Uygulanması M. Demiralp tarafından ortaya konarak ispatlanmış ve işlevi tek değişkenli bir fonksiyonun argümanını fonksiyonun kendisi ile çarpmak olan cebirsel bir operatörün matris gösteriliminin, aynı uzay ve aynı taban takımı altında argümanın matris gösteriliminin o fonksiyonun altındaki görüntüsüne eşit olduğunu ifade eden Sendelenimsizlik teoreminin, hata terimi integral biçiminde verilen Taylor açılımının hata terimine uygulanması söz konusudur. Elde edilen sonuçlar hata terimsiz Taylor açılımından elde edilenlerle karşılaştırılmıştır. Tek ve çok değişkenli integrasyon için ise fonksiyonun Taylor açılımı integre edilerek sendelenimsizlik uygulanmış ve böylelikle kuadratür benzeri yeni bir sayısal integrasyon metodu oluşturulmuştur. Sayısal sonuçlar hata terimsiz Taylor açılımının integrasyonundan elde edilenlerle karşılaştırılmış ve hataların analizi yapılmıştır.
Application of the Fluctuationlessness Theorem to the Approx-imation of Functions and Integration Based on the Fluctuationlessness theorem which was conjectured and proven by M. Demiralp, which states that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independent variable’s matrix representation over the same space via the same basis set, under that univariate function, when the fluctuation terms are ignored. Approximations to the functions of a single variable as well as to multivariable functions are made by using the Taylor expansion with the remainder term expressed in integral form. Results are compared with those obtained from the corresponding Taylor series expansion without the error term. As for the single and multivariable integration, the approximate expression obtained from the Taylor expansion is integrated and a new quadrature-like numerical integration method is obtained. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term, and errors are analyzed
Application of the Fluctuationlessness Theorem to the Approx-imation of Functions and Integration Based on the Fluctuationlessness theorem which was conjectured and proven by M. Demiralp, which states that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independent variable’s matrix representation over the same space via the same basis set, under that univariate function, when the fluctuation terms are ignored. Approximations to the functions of a single variable as well as to multivariable functions are made by using the Taylor expansion with the remainder term expressed in integral form. Results are compared with those obtained from the corresponding Taylor series expansion without the error term. As for the single and multivariable integration, the approximate expression obtained from the Taylor expansion is integrated and a new quadrature-like numerical integration method is obtained. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term, and errors are analyzed