希氏空间中算子样条插值及算子方程的近似解

Operator Spline Interpolations and the Approximate Solutions of Operator Equations on Hilbert Spaces

本文首先讨论希氏空间中由有界线性算子Ｔ确定的抽象插值样条（本文称Ｔ样条）的构造，通过引入新的内积得到Ｔ样条的投影特征和表达式．然后研究算子方程Ｔｘ＝ｙ的投影近似解和Ｔ样条近似解，并给出了两种近似解误差之间的关系．

This paper first discusses the structure of abstract interpolating splines (T- splines) associated with bounded linear operators. The projective property and the representation of T-spline are obtained by introducing a new inner product. Then the projective approximate solution and T-spline approximate solution of operator equation Tx=y are studied, and the relationships between the error estimates of the two approximate solutions are given.