Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a...Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.展开更多
Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation Au=f is solvable, and instead of knowing exactly f onl...Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation Au=f is solvable, and instead of knowing exactly f only know its approximation satisfies the condition: In this paper, we are interested a regularization method to solve the approximation solution of this equation. This approximation is a unique global minimizer of the functional , for any , defined as follows: . We also study the stability of this method when the regularization parameter is selected a priori and a posteriori. At the same time, we give an application of this method to the weak derivative operator equation in Hilbert space.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
文摘Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.
文摘Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation Au=f is solvable, and instead of knowing exactly f only know its approximation satisfies the condition: In this paper, we are interested a regularization method to solve the approximation solution of this equation. This approximation is a unique global minimizer of the functional , for any , defined as follows: . We also study the stability of this method when the regularization parameter is selected a priori and a posteriori. At the same time, we give an application of this method to the weak derivative operator equation in Hilbert space.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
