A novel recursive method to reconstruct multivariate functions on the unit cube

作者：Zhang, Zhihua^*

来源：Open Mathematics, 2017, 15(1): 1568-1577.

DOI：10.1515/math-2017-0132

• Recursive method
• Hyperbolic cross truncation
• Multivariate functions
• Fourier series

Due to discontinuity on the boundary, traditional Fourier approximation does not work efficiently for d-variate functions on [0, 1](d). In this paper, we will give a recursive method to reconstruct/approximate functions on [0, 1](d) well. The main process is as follows: We reconstruct a d-variate function by using all of its (d - 1)-variate boundary functions and few d-variate Fourier coefficients. We reconstruct each (d - 1)-variate boundary function given in the preceding reconstruction by using all of its (d - 2)-variate boundary functions and few (d - 1)-variate Fourier coeficients. Continuing this procedure, we finally reconstruct each univariate boundary function in the preceding reconstruction by using values of the function at two ends and few univariate Fourier coefficients. Our recursive method can reconstruct multivariate functions on the unit cube with much smaller error than traditional Fourier methods.

• 出版日期2017-12-29
• 单位北京师范大学