Given a compact linear operator $\K$, the (pseudo) inverse $\K^\dagger$ is usually substituted by a family of regularizing operators $\R_\alpha$ which depends on $\K$ itself. Naturally, in the actual computation we are forced to approximate the true continuous operator $\K$ with a discrete operator $\K^{(n)}$ characterized by a finesses discretization parameter $n$, and obtaining then a discretized family of regularizing operators $\R_\alpha^{(n)}$. In general, the numerical scheme applied to discretize $\K$ does not preserve, asymptotically, the full spectrum of $\K$. In the context of a generalized Tikhonov-type regularization, we show that a graph-based approximation scheme that guarantees, asymptotically, a zero maximum relative spectral error can significantly improve the approximated solutions given by $\R_\alpha^{(n)}$. This approach is combined with a graph based regularization technique with respect to the penalty term.

翻译：根据一个紧凑线性操作员的美元(K$),美元(假币)的反折数通常被一个正规化操作员的家族的美元(R)/alpha美元(美元)所取代,这取决于美元本身。自然,在实际计算中,我们不得不与一个离散操作员的美元(K)美元(n)美元(美元)相近,其特征是罚款分解参数(n)美元,然后获得一个离散操作员的离散式组合($)美元(K)美元)。一般而言,用于离散操作员的数值方案并不以同样的方式保存美元的全部频谱。在通用的Tikhonov型正规化背景下,我们表明基于图形的近似率方案可以保证,从某种意义上说,一个最大为零的相对光谱错误可以大大改进$(R)/alpha ⁇ (n)美元)的近似解决办法。这种办法与基于图表的与刑罚术语的正规化技术相结合。