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Storage and Computational Costs.

We have collected the dominant costs of the simple Jacobi-Davidson approach, in terms of storage and floating point operations, in two tables. The costs are given for iteration ${m}$ of the algorithm:

Item Storage
Search space $2{m}$ $n$-vectors
Residual $2$ $n$-vector
Approx. eigenvector $1$ $n$-vector
Projected system $.5$ matrix of order ${m}$
Eigenvectors of proj. system $1$ matrix of order ${m}$
Correction equation Depends on selected solver

Action Work
Search basis ${m}+1$ dot products, ${m}$ updates in iteration ${m}$
Projected system ${m}$ dots
Eigensystem projected system $O({m}^3)$
Residual $1$ matrix-vector product, $1$ update
  or ${m}$-fold update
Approx. eigenvector ${m}$-fold update
Correction equation Depends on choice of solver



next up previous contents index
Next: Restart and Deflation Up: Basic Algorithm Previous: Basic Algorithm   Contents   Index
Susan Blackford 2000-11-20