Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems

Algorithm 1

RFSAI computation.

INPUT: nband, 𝛿_out,𝑑_out,𝜀_out,𝛿_in,𝑑_in,𝜀_in

Compute the first lower triangular factor: 𝐺_out=  FSAIout(𝐴,nband,𝛿_out,𝑑_out,𝜀_out)

Compute the product: 𝐴⁽¹⁾=𝐺_out𝐴𝐺^𝑇_out

Compute the second lower triangular factor: 𝐺_in=FSAI𝐴⁽¹⁾,𝛿_in,𝑑_in,𝜀_in