Information based complexity analysis in computing the solution of various practical problems is of great importance in recent years. The amount of discrete information required to compute the solution plays an important role in the computational complexity of the problem. Although this approach has been applied successfully for linear problems, no effort has been made in literature to apply it to nonlinear problems. This article addresses this problem by considering an efficient discretization scheme to discretize nonlinear ill-posed problems. We apply the discretization scheme in the context of a simplified Gauss–Newton iterative method and show that our scheme requires only less amount of information for computing the solution. The convergence analysis and error estimates are derived. Numerical examples are provided to illustrate the fact that the scheme can be implemented successfully. The theoretical and numerical study asserts that the scheme can be employed to nonlinear problems.

中文翻译：

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求解非线性不适定问题的有效离散方案

近年来，基于信息的复杂性分析在计算各种实际问题的解中具有重要意义。计算解决方案所需的离散信息量在问题的计算复杂性中起着重要作用。尽管这种方法已成功应用于线性问题，但文献中还没有努力将其应用于非线性问题。本文通过考虑一种有效的离散化方案来离散化非线性不适定问题来解决这个问题。我们在简化的高斯-牛顿迭代方法的背景下应用离散化方案，并表明我们的方案只需要较少的信息来计算解决方案。推导出收敛分析和误差估计。给出了数值例子说明该方案可以成功实施。理论和数值研究表明该格式可以用于非线性问题。