Uniform accuracy of eigenpairs from a shift‐invert Lanczos method
Ulrich L. Hetmaniuk, Richard B. Lehoucq · SIAM Journal on Matrix Analysis and Applications · 2006
This paper analyzes the accuracy of the shift‐invert Lanczos iteration for computing eigenpairs of the symmetric definite generalized eigenvalue problem. We provide bounds for the accuracy of the eigenpairs produced by shift‐invert Lanczos given a residual reduction. We discuss the implications of our analysis for practical shift‐invert Lanczos iterations. When the generalized eigenvalue problem arises from a conforming finite element method, we also comment on the uniform accuracy of bounds (independent of the mesh size h).