Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the co...Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.展开更多
Heterogeneous community entails a number of social groups that adopt similar/different social norms.In such community,new individuals who join a new social group should be able to decide with which group they could as...Heterogeneous community entails a number of social groups that adopt similar/different social norms.In such community,new individuals who join a new social group should be able to decide with which group they could assimilate based on their capabilities/values/manners.Otherwise,they would be penalized by other members in the group for violating some norms which they cannot comply.Using this approach,software agents would have better reasoning in simulating human society.In this paper,the authors propose a norms assimilation theory,in which a new agent attempts to assimilate with a social group’s norms.This theory builds an approach to norm assimilation,analyzes the cases for an agent to decide to assimilate with a social group and develops a mathematical model to measure the assimilation cost and the agent’s ability.The approach is developed based on the agent’s internal belief about its ability and desire,and its external belief about the cost of assimilating with a number of social groups.The significance of this research is two-fold.Firstly,the study paves the way to future design of intelligent systems,i.e.,software agents or robots,to closely mimic human social interactions.Secondly,the norm assimilation using agent-based system could be potentially utilized to simulate some social issues such as immigrants,new students,expatriate etc.The experiments that have been conducted demonstrate that an agent in the domain is able to calculate the assimilation cost and decide which social group to join.展开更多
文摘Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.
文摘Heterogeneous community entails a number of social groups that adopt similar/different social norms.In such community,new individuals who join a new social group should be able to decide with which group they could assimilate based on their capabilities/values/manners.Otherwise,they would be penalized by other members in the group for violating some norms which they cannot comply.Using this approach,software agents would have better reasoning in simulating human society.In this paper,the authors propose a norms assimilation theory,in which a new agent attempts to assimilate with a social group’s norms.This theory builds an approach to norm assimilation,analyzes the cases for an agent to decide to assimilate with a social group and develops a mathematical model to measure the assimilation cost and the agent’s ability.The approach is developed based on the agent’s internal belief about its ability and desire,and its external belief about the cost of assimilating with a number of social groups.The significance of this research is two-fold.Firstly,the study paves the way to future design of intelligent systems,i.e.,software agents or robots,to closely mimic human social interactions.Secondly,the norm assimilation using agent-based system could be potentially utilized to simulate some social issues such as immigrants,new students,expatriate etc.The experiments that have been conducted demonstrate that an agent in the domain is able to calculate the assimilation cost and decide which social group to join.
