某些广义迭代法的Stein－Rosenberg型定理与比较定理

STEIW-ROSENBERG TYPE THEORSMS AND COMMMSON THEOREMS FOR SOME GENERALIZED ITERAIVE METHODS

某些广义迭代法的Ｓｔｅｉｎ－Ｒｏｓｅｎｂｅｒｇ型定理与比较定理王新民（中国金融学院）ＳＴＥＩＷ－ＲＯＳＥＮＢＥＲＧＴＹＰＥＴＨＥＯＲＳＭＳＡＮＤＣＯＭＭＭＳＯＮＴＨＥＯＲＥＭＳＦＯＲＳＯＭＥＧＥＮＥＲＡＬＩＺＥＤＩＴＥＲＡＩＶＥＭＥＴＨＯＤＳ￥Ｗａｎ...

The paper discusses the generalized AOR(and SOR) and TOR iterative methods, provides a counterexample of the Stein-Rosenberg type theorems for these generalized iterative methods given in [3, 7, 9, 13]. Following our idea in [4] in which the Stein-Rosenberg type theorems were established for the generalized it erative methods with the iteration matrix M-1N, we renew the Stein-Rosenberg theorems and develop its sharp forms for the generalized AOR and TOR iterative methods, point out the sufficient and necessary conditions for the corresponding propositions given in [3, 7, 9, 13], and give the comparison theorems for these generalized iterative methods, containing and extending the previous results given in [10, 13, 15]. Finallyl a set of sufficient and necessary conditions are given to determine that A is an M-matrix.