基于小波收缩求解时间反向热传导问题的正则化方法  

Regularization method for solving a backward heat conduction problem based on wavelet shrinkage

作　　者：庄娥 熊向团 薛雪敏 马小军 ZHUANG E;XIONG Xiangtuan;XUE Xuemin;MA Xiaojun(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《应用数学与计算数学学报》2018年第4期831-840,共10页Communication on Applied Mathematics and Computation

基　　金：西北师范大学科学计算创新团队资助项目(NWNU-LKQN-17-5)

摘　　要：时间反向热传导问题是一类典型的不适定问题.应用对偶最小二乘法给出了时间反向热传导问题的误差估计,同时用小波收缩方法给出了它的非线性近似解的误差估计,并证明了在高层上的收敛性.The backward heat conduction problem in time is a typical ill-posed problem.We apply a wavelet dual least squares method to a backward heat equation,and the error estimate between the approximate solution and the exact solution is given.The error estimate between the nonlinear approximate solution and the exact solution is given by the wavelet shrinkage method,which proves the method converges at a high level.

关 键 词：反向热传导问题 不适定问题 Meyer小波 最小二乘法 非线性收缩 正则化 

分 类 号：O241.5[理学—计算数学]