In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Conver...In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine.Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes,numerical experiments and CPU time-methodology.Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods.Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples.Numerical test examples,dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.展开更多
In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: t...In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: that of the lost decade, that of 2008 and that of the Covid-19 pandemic. To this end, they use a particular type of mathematical-statistical model that is widely applied today in the economic field, namely a simultaneous equation model (SEM). This simultaneous equation model is estimated through an Iteratively reweighted least squares (IRLS) using quarterly historical series in the sample period Q1 1994 - Q2 2020. All data are in real terms. The results, appropriately compared with those of other authors, suggest that the monetary policy has a (limited) impact only on the interbank market. The fiscal policy, instead, has a greater ability to influence the money supply, the private consumption and the inflation expectations.展开更多
This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the imp...This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. 4 numerical example by descent method is given.展开更多
Income and expenditure are highlighted in this study as they currently affect the quality of life of the Malaysian society. In the Ninth Malaysia Plan （2006-2010） poverty eradication was emphasized as one of the soc...Income and expenditure are highlighted in this study as they currently affect the quality of life of the Malaysian society. In the Ninth Malaysia Plan （2006-2010） poverty eradication was emphasized as one of the socio-economic targets to uplift those poor households from the fast moving modern sectors of the economy. The primary objective of this paper is therefore to identify income and expenditure relationships among the households of the east coast of Peninsular Malaysia during the current economic downturn. Attempts to analyze household consumption as a share of total income and to identify factors contributing to household income and expenditure have become a topic of interest in literature. A substantial portion of household income devoted to productive loans characterizes the majority of Malaysians as the economy progresses to a more advance stage. A significant and strong relationship between income and types of household expenditure is explored from the socio-economic perspectives. Using primary data a system of simultaneous equations, namely the two stage least squares （2SLS） was applied. This paper identifies crucial variables associated with the income and expenditure. Some of these variables showing high correlation with the total expenditure are the housing loan, automobile loan and educational expenditure.展开更多
This study develops crash rate prediction models based on the premise that crash frequencies observed from adjacent paired non-weaving and weaving freeway segments are spatially correlated and therefore requires a sim...This study develops crash rate prediction models based on the premise that crash frequencies observed from adjacent paired non-weaving and weaving freeway segments are spatially correlated and therefore requires a simultaneous equation modeling approach. Simultaneous equation models for paired freeway non-weaving segments and weaving segments along with combined three freeway segments upstream and downstream were developed to investigate the relationship of crash rate with freeway characteristics. The endogenous variables have significant coefficients which indicate that unobserved variables exist on these contiguous segments, resulting in different crash rates. AADT is a variable that can show the interaction between the traffic and crashes on these contiguous segments. The results corroborate such an interaction. By comparing the simultaneous equation model and the multiple linear regression model, it is shown that more model parameters in the simultaneous models are significant than those from linear regression model. This demonstrates the existence of the correlation between the interchange and between-interchange segments. It is crucial that some variables like segment length can be identified significant in the simultaneous model, which provides a way to quantify the safety impact of freeway development.展开更多
On the basis of using entropy weight method to measure China’s education poverty alleviation and rural revitalization evaluation indicators, using the panel data of 30 provinces in China (excluding Xizang, Hong Kong,...On the basis of using entropy weight method to measure China’s education poverty alleviation and rural revitalization evaluation indicators, using the panel data of 30 provinces in China (excluding Xizang, Hong Kong, Macao and Taiwan) from 2012 to 2021, a spatial panel simultaneous equation model is constructed based on adjacency matrix, geographical distance matrix and economic geographical distance matrix deeply study the interaction mechanism and spatial spillover effects between education poverty alleviation and rural revitalization through the generalized spatial three-stage least squares method (GS3SLS). The results indicate that there is a significant spatial spillover effect and a positive spatial correlation between education poverty alleviation and rural revitalization, and there is a significant interactive effect between the two variables, while promoting each other positively. Therefore, the government should clarify the deep relationship between education poverty alleviation and rural revitalization based on the current background, and better consolidate and expand the effective connection between the achievements of education poverty alleviation and rural revitalization.展开更多
Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume...Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine （Pinus massoniana Lamb.） in southern China, we constructed one-, two- and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations by using error-in-variable simultaneous equations. The prediction precision of aboveground biomass estimates from one variable equa- tion exceeded 95%. The regressions of aboveground biomass equations were improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically insignificant. For the biomass conversion function on one variable, the conversion factor decreased with increasing diameter, but for the conversion function on two variables, the conversion factor increased with increasing diameter but decreased with in- creasing tree height.展开更多
Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chine...Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.展开更多
The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equation...The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equations to model point neutron kinetics.The nested approach is the most common method to solve DAE,but this approach is very expensive and time-consuming due to inner iterations.This paper deals with an alternative approach in which a simultaneous solution method is used.The DAEs are discretized over a time horizon using collocation on finite elements,and Radau collocation points are applied.The resulting nonlinear algebraic equations can be solved by existing solvers.The discrete algorithm is discussed in detail;both accuracy and stability issues are considered.Finally,the simulation results are presented to validate the efficiency and accuracy of the simultaneous approach that takes much less time than the nested one.展开更多
In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the con...In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.展开更多
This paper presents an procedure for purifying training data sets （i.e., past occurrences of slope failures） for inverse estimation on unobserved trigger factors of ＂different types of simultaneous slope failures＂...This paper presents an procedure for purifying training data sets （i.e., past occurrences of slope failures） for inverse estimation on unobserved trigger factors of ＂different types of simultaneous slope failures＂. Due to difficulties in pixel-by-pixel observations of trigger factors, as one of the measures, the authors had proposed an inverse analysis algorithm on trigger factors based on SEM （structural equation modeling）. Through a measurement equation, the trigger factor is inversely estimated, and a TFI （trigger factor influence） map can be also produced. As a subsequence subject, a purification procedure of training data set should be constructed to improve the accuracy of TFI map which depends on the representativeness of given training data sets of different types of slope failures. The proposed procedure resamples the matched pixels between original groups of past slope failures （i.e., surface slope failures, deep-seated slope failures, landslides） and classified three groups by K-means clustering for all pixels corresponding to those slope failures. For all cases of three types of slope failures, the improvement of success rates with respect to resampled training data sets was confirmed. As a final outcome, the differences between TFI maps produced by using original and resampled training data sets, respectively, are delineated on a DIF map （difference map） which is useful for analyzing trigger factor influence in terms of ＂risky- and safe-side assessment＂ sub-areas with respect to ＂different types of simultaneous slope failures＂.展开更多
Prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in thes...Prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in these approximations increases with increasing angle of incidence and variation of the elastic parameters, which increases the number of inversion solutions and minimizes the inversion accuracy. In this study, we explore a method for solving the reflection coefficients by using the Zoeppritz equations. To increase the accuracy of prestack inversion, the simultaneous inversion of P-wave velocity, S-wave velocity, and density by using prestack large-angle seismic data is proposed based on generalized linear inversion theory. Moreover, we reduce the ill posedness and increase the convergence of prestack inversion by using the regularization constraint damping factor and the conjugate gradient algorithm. The proposed prestack inversion method uses prestack large-angle seismic data to obtain accurate seismic elastic parameters that conform to prestack seismic data and are consistent with logging data from wells.展开更多
波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风...波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。展开更多
基金the Natural Science Foundation of China(Grant Nos.61673169,11301127,11701176,11626101,and 11601485)The Natural Science Foundation of Huzhou City(Grant No.2018YZ07).
文摘In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine.Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes,numerical experiments and CPU time-methodology.Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods.Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples.Numerical test examples,dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.
文摘In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: that of the lost decade, that of 2008 and that of the Covid-19 pandemic. To this end, they use a particular type of mathematical-statistical model that is widely applied today in the economic field, namely a simultaneous equation model (SEM). This simultaneous equation model is estimated through an Iteratively reweighted least squares (IRLS) using quarterly historical series in the sample period Q1 1994 - Q2 2020. All data are in real terms. The results, appropriately compared with those of other authors, suggest that the monetary policy has a (limited) impact only on the interbank market. The fiscal policy, instead, has a greater ability to influence the money supply, the private consumption and the inflation expectations.
基金Scientific Foundation of South China Unviersity of Technology
文摘This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. 4 numerical example by descent method is given.
文摘Income and expenditure are highlighted in this study as they currently affect the quality of life of the Malaysian society. In the Ninth Malaysia Plan （2006-2010） poverty eradication was emphasized as one of the socio-economic targets to uplift those poor households from the fast moving modern sectors of the economy. The primary objective of this paper is therefore to identify income and expenditure relationships among the households of the east coast of Peninsular Malaysia during the current economic downturn. Attempts to analyze household consumption as a share of total income and to identify factors contributing to household income and expenditure have become a topic of interest in literature. A substantial portion of household income devoted to productive loans characterizes the majority of Malaysians as the economy progresses to a more advance stage. A significant and strong relationship between income and types of household expenditure is explored from the socio-economic perspectives. Using primary data a system of simultaneous equations, namely the two stage least squares （2SLS） was applied. This paper identifies crucial variables associated with the income and expenditure. Some of these variables showing high correlation with the total expenditure are the housing loan, automobile loan and educational expenditure.
文摘This study develops crash rate prediction models based on the premise that crash frequencies observed from adjacent paired non-weaving and weaving freeway segments are spatially correlated and therefore requires a simultaneous equation modeling approach. Simultaneous equation models for paired freeway non-weaving segments and weaving segments along with combined three freeway segments upstream and downstream were developed to investigate the relationship of crash rate with freeway characteristics. The endogenous variables have significant coefficients which indicate that unobserved variables exist on these contiguous segments, resulting in different crash rates. AADT is a variable that can show the interaction between the traffic and crashes on these contiguous segments. The results corroborate such an interaction. By comparing the simultaneous equation model and the multiple linear regression model, it is shown that more model parameters in the simultaneous models are significant than those from linear regression model. This demonstrates the existence of the correlation between the interchange and between-interchange segments. It is crucial that some variables like segment length can be identified significant in the simultaneous model, which provides a way to quantify the safety impact of freeway development.
文摘On the basis of using entropy weight method to measure China’s education poverty alleviation and rural revitalization evaluation indicators, using the panel data of 30 provinces in China (excluding Xizang, Hong Kong, Macao and Taiwan) from 2012 to 2021, a spatial panel simultaneous equation model is constructed based on adjacency matrix, geographical distance matrix and economic geographical distance matrix deeply study the interaction mechanism and spatial spillover effects between education poverty alleviation and rural revitalization through the generalized spatial three-stage least squares method (GS3SLS). The results indicate that there is a significant spatial spillover effect and a positive spatial correlation between education poverty alleviation and rural revitalization, and there is a significant interactive effect between the two variables, while promoting each other positively. Therefore, the government should clarify the deep relationship between education poverty alleviation and rural revitalization based on the current background, and better consolidate and expand the effective connection between the achievements of education poverty alleviation and rural revitalization.
基金the National Biomass Modeling Program for Continuous Forest Inventory(NBMP-CFI) funded by the State Forestry Administration of China
文摘Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine （Pinus massoniana Lamb.） in southern China, we constructed one-, two- and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations by using error-in-variable simultaneous equations. The prediction precision of aboveground biomass estimates from one variable equa- tion exceeded 95%. The regressions of aboveground biomass equations were improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically insignificant. For the biomass conversion function on one variable, the conversion factor decreased with increasing diameter, but for the conversion function on two variables, the conversion factor increased with increasing diameter but decreased with in- creasing tree height.
基金supported by the Agricultural Science and Technique Foundation of Guizhou Province, China (No. 2008-3059)the Research Funds of Forestry Administration of Guizhou Province, China (Nos. 2010-01-08, 2010-01, 200625)
文摘Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.
基金Project supported by the National Basic Research Program of China (No. 2009CB320603)the National Natural Science Foundation of China (Nos. 60974007 and 60934007)
文摘The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equations to model point neutron kinetics.The nested approach is the most common method to solve DAE,but this approach is very expensive and time-consuming due to inner iterations.This paper deals with an alternative approach in which a simultaneous solution method is used.The DAEs are discretized over a time horizon using collocation on finite elements,and Radau collocation points are applied.The resulting nonlinear algebraic equations can be solved by existing solvers.The discrete algorithm is discussed in detail;both accuracy and stability issues are considered.Finally,the simulation results are presented to validate the efficiency and accuracy of the simultaneous approach that takes much less time than the nested one.
文摘In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.
文摘This paper presents an procedure for purifying training data sets （i.e., past occurrences of slope failures） for inverse estimation on unobserved trigger factors of ＂different types of simultaneous slope failures＂. Due to difficulties in pixel-by-pixel observations of trigger factors, as one of the measures, the authors had proposed an inverse analysis algorithm on trigger factors based on SEM （structural equation modeling）. Through a measurement equation, the trigger factor is inversely estimated, and a TFI （trigger factor influence） map can be also produced. As a subsequence subject, a purification procedure of training data set should be constructed to improve the accuracy of TFI map which depends on the representativeness of given training data sets of different types of slope failures. The proposed procedure resamples the matched pixels between original groups of past slope failures （i.e., surface slope failures, deep-seated slope failures, landslides） and classified three groups by K-means clustering for all pixels corresponding to those slope failures. For all cases of three types of slope failures, the improvement of success rates with respect to resampled training data sets was confirmed. As a final outcome, the differences between TFI maps produced by using original and resampled training data sets, respectively, are delineated on a DIF map （difference map） which is useful for analyzing trigger factor influence in terms of ＂risky- and safe-side assessment＂ sub-areas with respect to ＂different types of simultaneous slope failures＂.
基金supported by the 973 Program of China(No.2011CB201104 and 2011ZX05009)the National Science and the Technology Major Project(No.2011ZX05006-06)
文摘Prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in these approximations increases with increasing angle of incidence and variation of the elastic parameters, which increases the number of inversion solutions and minimizes the inversion accuracy. In this study, we explore a method for solving the reflection coefficients by using the Zoeppritz equations. To increase the accuracy of prestack inversion, the simultaneous inversion of P-wave velocity, S-wave velocity, and density by using prestack large-angle seismic data is proposed based on generalized linear inversion theory. Moreover, we reduce the ill posedness and increase the convergence of prestack inversion by using the regularization constraint damping factor and the conjugate gradient algorithm. The proposed prestack inversion method uses prestack large-angle seismic data to obtain accurate seismic elastic parameters that conform to prestack seismic data and are consistent with logging data from wells.
文摘波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。
