SOLUTION OF SYSTEMS OF COMPLEX LINEAR-EQUATIONS IN THE L-INFINITY NORM WITH CONSTRAINTS ON THE UNKNOWNS

作     者：STREIT, RL 

作者机构：STANFORD UNIVDEPT OPERAT RESSTANFORDCA 94305 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1986年第7卷第1期

页      面：132-149页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：complex linear equations Chebyshev solution convex constraints complex approximation semi-infinite programming l∞ norm 

摘      要：An algorithm for the numerical solution of general systems of complex linear equations in the $l_\infty $, or Chebyshev, norm is presented. The objective is to find complex values for the unknowns so that the maximum magnitude residual of the system is a minimum. The unknowns are required to satisfy certain convex constraints; in particular, bounds on the magnitudes of the unknowns are imposed. In the algorithm presented here, this problem is replaced by a linear program generated in such a way that the relative error between its solution and a solution of the original problem can be estimated. The maximum relative error can easily be made as small as desired by selecting an appropriate linear program. Order of magnitude improvements in both computation time and computer storage requirements in an implementation of the simplex algorithm to this linear program are presented. Three numerical examples are included, one of which is a complex function approximation problem.