贺国强
Abstract
Let X and Y be real Hilbert spaces and A: X→Y be a bounded linear operator with nonclosed range R(A). If y∈ D(A~+)=R(A)+R(A)~⊥, there exists a unique Moore-Penrose generalized solution to the equation Ax=y. In practice, however, the given equation is usually of an approximate form Ax=yδ, (1)
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Let X and Y be real Hilbert spaces and A: X→Y be a bounded linear operator with nonclosed range R(A). If y∈ D(A~+)=R(A)+R(A)~⊥, there exists a unique Moore-Penrose generalized solution to the equation Ax=y. In practice, however, the given equation is usually of an approximate form Ax=yδ, (1)
Key concepts: Tikhonov regularization, Iterated function, Mathematics, Hilbert space, Bounded function, Regularization (linguistics), A priori and a posteriori, Operator (biology)