A Non-conditional Uniform Divergence Criteria of Projection Method for Compact Operator Equation

11/24/2019

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by   Yidong Luo, et al.

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Projection methods (including collocation methods) are always considered in numerical analysis for differential and integral equations Ax=b. It is regular to restrict the consideration to b ∈R(A) which make the equation solvable. In this paper, we project more insight to the numerical behavior of projection methods when b ∉R(A) and propose an non-conditional divergence result of projection method with arbitrary basis into compact operator equation (Theorem 1.1). Several applications show its power and further discussion on divergence rate is given.