## Version 1.4.1

18th November 2021

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### EA16: Compute selected eigenpairs using rational Lanczos method

EA16 uses an implicitly restarted block Lanczos method or rational Lanczos method to compute selected eigenpairs of large sparse real eigenproblems. EA16 may be used to compute approximate eigenpairs for the following problems:

1. Standard eigenvalue problem : $$\mathbf{Ax} = \lambda \mathbf{x}$$, $$\mathbf{A}$$ sparse symmetric.

2. Generalised eigenvalue problem : $$\mathbf{Ax} = \lambda \mathbf{Mx}$$, $$\mathbf{A}$$ sparse symmetric, $$\mathbf{M}$$ sparse symmetric positive (semi) definite.

3. Buckling problem : $$\mathbf{Ax} = \lambda \mathbf{Mx}$$, $$\mathbf{A}$$ sparse symmetric positive (semi) definite, $$\mathbf{M}$$ sparse symmetric.

Precision: At least 8-byte arithmetic is recommended.