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提出了用变形的Fourier部分和来代替Fourier级数将输入数据光滑的一种新方法。该方法能稳定地解某些不适定的问题,如给定函数的近似,求函数微分的问题;Laplace方程Cauchy问题;时间逆向热传导方程的Cauchy问题等。
A new method of smoothing the input data by using the Fourier part of the transformation and instead of the Fourier series is proposed. This method can stably solve some ill-posed problems, such as the approximation of a given function, the problem of finding the differential of a function, the Cauchy problem of the Laplace equation, the Cauchy problem of the time inverse heat conduction equation, and so on.