房价预测、共享单车出租数量预测、空气污染情况预测等常涉及矛盾方程组求解,对其数值求解方法研究具有重要的理论意义与应用价值。当矛盾方程组规模过大时,用传统的最小二乘法求解,不仅计算量大,而且由于误差积累使最终结果的准确性不...房价预测、共享单车出租数量预测、空气污染情况预测等常涉及矛盾方程组求解,对其数值求解方法研究具有重要的理论意义与应用价值。当矛盾方程组规模过大时,用传统的最小二乘法求解,不仅计算量大,而且由于误差积累使最终结果的准确性不高。鉴于此,采用机器学习中的最小二乘支持向量机(least squares support vector machine,LS-SVM)算法求解大规模矛盾方程组,并分别针对线性、非线性、单变量、多变量矛盾方程组进行了数值求解。数值结果表明,数据类型和数据量的变化对结果的影响不大,因此只要选取适当的参数就可建立合适的模型,得到高精度的预测结果。展开更多
Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced...Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.展开更多
文摘房价预测、共享单车出租数量预测、空气污染情况预测等常涉及矛盾方程组求解,对其数值求解方法研究具有重要的理论意义与应用价值。当矛盾方程组规模过大时,用传统的最小二乘法求解,不仅计算量大,而且由于误差积累使最终结果的准确性不高。鉴于此,采用机器学习中的最小二乘支持向量机(least squares support vector machine,LS-SVM)算法求解大规模矛盾方程组,并分别针对线性、非线性、单变量、多变量矛盾方程组进行了数值求解。数值结果表明,数据类型和数据量的变化对结果的影响不大,因此只要选取适当的参数就可建立合适的模型,得到高精度的预测结果。
基金supported by the Natural Science Foundation of China (Nos. 11971230, 12071215)the Fundamental Research Funds for the Central Universities(No. NS2018047)the 2019 Graduate Innovation Base(Laboratory)Open Fund of Jiangsu Province(No. Kfjj20190804)
文摘Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.
