In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具...设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具误差的 Ishikawa 迭代序列强收敛到方 程 Tx = f 的唯一解。本文结果推广和发展了现有的相应结果。展开更多
基金This work was supported by the National Natural Sciences Foundation P. R. China, (No. 19871029) and the City Foundation of Shanghai for Selected Academic Reseach.
文摘In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
文摘设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具误差的 Ishikawa 迭代序列强收敛到方 程 Tx = f 的唯一解。本文结果推广和发展了现有的相应结果。
