Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters a...Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.展开更多
A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems...A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.展开更多
文摘Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
基金supported by the National Natural Science Foundation of China (No. 11071033)the Fundamental Research Funds for the Central Universities (No. 090405013)
文摘A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.
