Abstract
Abstract We give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between T † T ( X n ) {T^{\dagger}T(X_{n})} and T * T ( X n ) {T^{*}T(X_{n})} , and the principal angles between X n ∩ ( 𝒩 ( T ) ∩ X n ) ⊥ {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and ( 𝒩 ( T ) + X n ) ∩ 𝒩 ( T ) ⊥ {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}} . At the end, we consider several specific cases and examples to further illustrate our theorems.
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