2009年12月1日，是梁学章先生的70华诞．在这个特殊的日子来临之际，编者通过吉林大学出版社出版了《梁学章教授数学文选》，以作庆祝。

《梁学章教授数学文选》在附录中收录了先生当年硕士毕业论文的部分章节，这部分内容无疑是先生青年时代的得意之作。

前言 

1．二元插值多项式的收敛性

2．二元插值的适定结点组与迭加插值法

3．关于多元函数的插值与逼近

4．构造二元切触插值公式的方法

5．On Bivariate Osculatory Interpolation，

6．Lagrange Interpolation On a Sphere，Northeast

7．Properly Posed Sets of Nodes for Multivariate Lagrange Interpolation in俨，

8．The Application of Cayley-Bacharach Theorem to Bivariate Lagrange Interpolation

9．多元Lagrange插值与Cayley-Bacharach定理

10．Some Researches on Rrivariate Lagrange Interpolation11．Multivariate Lagrange Interpolation and an Application of Cayley-Bacharach Theorem for It

12．高维空间中代数流形上多项式空间的维数与Lagrange插值适定结点组的构造

13．Some Researches on Multivariate Lagrange Interpolation along the Sufficiently Intersected Algebraic Manifold

14．A Kind of Laange Interpolation on the Sphere．2009 WRI World Congress on Computer Science and Information Engineering．

15．On Lagrange and Hermite Interpolation Along Algebraic Manifold

16．Superposition Interpolation Process in C”

17．On Hakopian Interpolation in the Disk；Approx．

18．Kergin Interpolation at the Points Which Are Zeros of the Bivariate Polynomial of Least Deviation from Zero on the Disk：

19．Lagrange Representation of Multivariate Interpolation

20．关于圆域上Kergin插值的收敛性

21．On the Convergence of Hakopian Interpolation and Cubature

22．On the Integral Convergence of Kergin Interpolation on the Disk

23．On the Uniform Convergence of Kergin Interpolation on the Disk，

24．A New Algorithm for CT Based on Hakopian Interpolation．

25．基于Hakopian插值的快速图像重建算法

26．Weighted Mean Convergence of Hakopian Interpolation on the Disk．

27．关于多元■逼近(I)

28．关于多元■逼近(II)

29．某些高维区域上的最小零偏差多项式

30．On Chebyshev Approximation in Several Variables(III)，Approximation，Optimization and Computing：Theory and Applications．

31．基于圃域上多项式逼近的图像重建算法

32．Analysis and Improvement of Marr’S Algorithm for Image Reconstruction：

33．平行六边形域上的二重Fourier级数的线性求和

34．Convergence Properties of Generalized Fourier Series Oil a Parallel HexagonDomain，Comm

35．二元四次样条插值与有限元

36．关于高精度样条插值公式的一点注记

37．等距结点上一类新的样条插值公式

38．关于二元四次样条插值

39．两邻接州mBS曲面问的G2连续条件

40．G2Continuity Conditions for Two Adjacent B-spline Surfaces

41．G1Continuity Conditions of Adjacent NURBS Surfaces

42．G1Smooth ConnectionofAdjacent NURBS Surfaces

43．G1Smooth NUllS Surfaces with n-patch Comer

44．The Construction of G1 Smooth NURBS Surfaces over Arbitrary Topology Type．

45．B样条曲面问G1连续条件及局部格式构造问题

46．由点云数据生成三角网格曲面的区域增长算法

47．用Loop细分曲面拟合点云数据的方法

48．The Smooth Connection Algorithm between B-spline Surfaces Patches，

49．Loop细分小波紧框架对三维图形压缩的应用

50．Bivariste Box-spline Wavelets，M．Cheng et以(eds．)，Harmonic Analysis in China．

51．Real-valued Periodic Wavelets：Construction and Relation with Fourier Series

52．How to Get the Original Discrete Approximation for the Pyramid Algorithm of Multiresolution Decomposition

53．区同上的双正交小波的一种构造方法，高等学校计算数学学报

54．SolvSecond Kind Integral Equations by Galerkin Methods with Continuous Orthogonal Wavelets，J．Comput．Appl．Math

55．A Wavelet-based Ddtal Watermarking Algorithm，Proceedings of the International Conference on Wavelet Analysis and Its Applications

56．Bivariate Real-valued Orthogonal Periodic Box-spUne Wavelets，Northeast

57．Mammographic Image Enhancement and Denoting Based on Redundent Wavelet Transform，Proceedings of the International Conference 2006 Oil Wavelet Active Media Technology and Information Processing，

58．An Implementation of Fast Algorithm,q for Biorthogonal Periodic Interpolatory Wavelets，J．Inform．Comput．

59．A New Algorithm For Enhancing the Contrast of Finger-vein image

60．2D Chaotic Watermark Generation Based on Wavelet Transform and Bivariate Logistic Model，International Conference on Complex Systems and Applications

附录 多元插值的适定结点组与叠加插值法

论文和著作总目录