Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.
The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can b...We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.展开更多
文摘Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.
基金This project is supported by the Special Funds for Major State Basic Research Projects(Grant No. G19990328) the National Natural Science Foundation of China(Grant No. 10271025) also supported partly by Zhejiang Provincial Natural Science Foundation o
文摘The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
文摘We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.
