Research on emile borel ' s work on improving lagrange interpolation polynomial 對(duì)波萊爾改進(jìn)拉格朗日插值公式思想方法的研究
Convergence order of double variate combination trigonometric interpolation polynomials 二元組合型三角插值多項(xiàng)式的收斂階
The trigonometric interpolation polynomials ' simultaneous approximation of functions and their derivatives 三角插值多項(xiàng)式對(duì)函數(shù)及其導(dǎo)數(shù)的同時(shí)逼近
The errors in calculating derivatives for the gll collocation points are evaluated , which can be alleviated from o ( ( n4 ) to o ( ( n2 ) by the double - precision method proposed in the present paper , where ( denotes the machine precision and n the order of the interpolation polynomials in the elements 文中對(duì)gll配置點(diǎn)下的求導(dǎo)誤差進(jìn)行了分析,提出的雙精度方法可以將求導(dǎo)誤差從o ( ( n4 )減小到o ( ( n2 ) ,其中(為機(jī)器精度, n為單元內(nèi)插值多項(xiàng)式階數(shù)。
In the terms of interpolation , the image reconstructed from nearest interpolation or linear interpolation has good edge but serious noise ; reconstruction from 4 * 4cubic interpolation or three b - spline or three - order lagrange interpolations has better local character . 2 x 2cubic interpolations which has both better edge and local character is the ideal interpolation , the following is the basic principle during reconstruction : ( 1 ) the more width of interpolation , the more number of summation and the more order of interpolation polynomial , the higher of density resolution ; ( 2 ) the more of interpolation polynomial and width of interpolation , the more of reconstruction time simultaneously , aimed at eliminating the effects of noise contained in projection data , in this paper , author analysis cause and effects of common artifacts . importantly , discusses convolution back - projection reconstruction algorithm with a shift axis of rotation has been derived for correcting images that acquired with a divergence axis of rotation using the fan beam geometry with an angle - equaled detector 在ct圖像重建時(shí),選擇有限帶寬窗有較好的空間分辨率,三角形窗有較好的密度分辨率,選擇余弦窗則使得空間分辨率與密度分辨率的折衷;從窗函數(shù)的頻譜角度來(lái)講,可以用于圖像重建的一個(gè)良好的卷積窗函數(shù)應(yīng)該具備以下條件: ( ? )小的3db帶寬b ,即最小的主瓣寬度; ( ? )最小的旁瓣最大峰值a ; ( ? )最大的旁瓣峰值衰減速度d ;就內(nèi)插函數(shù)而言,臨近點(diǎn)內(nèi)插與線性?xún)?nèi)插重建圖像噪聲大,但有較好的邊緣與細(xì)節(jié); 4 4三次內(nèi)插、三次b -樣條與四次拉格朗日多項(xiàng)式內(nèi)插圖像平滑,局部特性較好。
A kind of operator of trigonometric interpolation polynomials with bivariate product was constructed based on an equidistant node set , so that the operator could be converged uniformly to bivariate continuous functions with periodicity of 27 on whole plane , and the convergence order of the approximation would be optimal for a body of functions with arbitrary - ordered continuous partial deritives 摘要構(gòu)造了一類(lèi)基于等距結(jié)點(diǎn)組上的二元三角插值多項(xiàng)式算子,使得該算子在全平面上一致收斂到每個(gè)以2為周期的二元連續(xù)函數(shù),并且對(duì)具有任意階連續(xù)偏導(dǎo)數(shù)的函數(shù)全體的逼近具有最佳收斂階。