As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared to...As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.展开更多
Bivariate vector valued rational interpolants are established by means of Thiele-type branched continued fractions and Samelson inverse over rectangular grids with holes, characterisation theorem with topologic struct...Bivariate vector valued rational interpolants are established by means of Thiele-type branched continued fractions and Samelson inverse over rectangular grids with holes, characterisation theorem with topologic structure is brought in light and uniqueness theorem in some sense is obtained.展开更多
基于卷积神经网络的图像超分辨率重建算法是数字图像处理领域近年来的研究热点。针对低分辨率图像在预处理时使用双三次插值导致图像丢失一些重要的高频纹理细节以及网络模型优化问题,文章提出了连分式插值结合卷积神经网络的超分辨率...基于卷积神经网络的图像超分辨率重建算法是数字图像处理领域近年来的研究热点。针对低分辨率图像在预处理时使用双三次插值导致图像丢失一些重要的高频纹理细节以及网络模型优化问题,文章提出了连分式插值结合卷积神经网络的超分辨率重建方法。在原有的轻量级基于卷积神经网络的超分辨率重建算法(super-resolution convolutional neural net work,SRCNN)网络模型基础上,首先采用Newton-Thiele型连分式插值函数将低分辨率图像插值到目标尺寸;然后利用3个卷积层进行图像特征提取、非线性映射、重建与优化;该文在网络收敛时利用Radam优化算法自适应地调整梯度,并且采用余弦衰减法逐渐降低学习率。实验结果表明,该网络模型能够在轻量级的卷积神经网络下获得更丰富的纹理细节和更清晰的图像边缘。展开更多
Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms ...Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,展开更多
Two classes of general bivariate interpolating frames are established by introducing multiple parameters. Many well known interpolating schemes, such as Newtoninterpolation, branched continued fraction interpolation ...Two classes of general bivariate interpolating frames are established by introducing multiple parameters. Many well known interpolating schemes, such as Newtoninterpolation, branched continued fraction interpolation proposed by Siemaszko and symmetric continued fraction interpolation considered by Cuyt and Murphy, can be obtainedby choosing proper parameters in our results.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10171026 and in part by the Foundation for Excellent Young Teachers of the Ministry of Education of China and the Financially-Aiding Program for the Backbone Teachers of the Min
文摘As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.
文摘Bivariate vector valued rational interpolants are established by means of Thiele-type branched continued fractions and Samelson inverse over rectangular grids with holes, characterisation theorem with topologic structure is brought in light and uniqueness theorem in some sense is obtained.
文摘基于卷积神经网络的图像超分辨率重建算法是数字图像处理领域近年来的研究热点。针对低分辨率图像在预处理时使用双三次插值导致图像丢失一些重要的高频纹理细节以及网络模型优化问题,文章提出了连分式插值结合卷积神经网络的超分辨率重建方法。在原有的轻量级基于卷积神经网络的超分辨率重建算法(super-resolution convolutional neural net work,SRCNN)网络模型基础上,首先采用Newton-Thiele型连分式插值函数将低分辨率图像插值到目标尺寸;然后利用3个卷积层进行图像特征提取、非线性映射、重建与优化;该文在网络收敛时利用Radam优化算法自适应地调整梯度,并且采用余弦衰减法逐渐降低学习率。实验结果表明,该网络模型能够在轻量级的卷积神经网络下获得更丰富的纹理细节和更清晰的图像边缘。
基金Supported by-the National Natural Science Foundation of China
文摘Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,
基金Supported by the National Science Foundation of China
文摘Two classes of general bivariate interpolating frames are established by introducing multiple parameters. Many well known interpolating schemes, such as Newtoninterpolation, branched continued fraction interpolation proposed by Siemaszko and symmetric continued fraction interpolation considered by Cuyt and Murphy, can be obtainedby choosing proper parameters in our results.
