GEPP Growth

\(n \times n\) extensions of matrices of the form

\[\begin{split}A = \begin{pmatrix} 1 & 0 & 0 & 1 \\ -1 & 1 & 0 & 1 \\ -1 &-1 & 1 & 1 \\ -1 &-1 &-1 & 1 \end{pmatrix}\end{split}\]

were known by Wilkinson to lead to an element-growth factor of \(2^{n-1}\) for Gaussian Elimination with Partial Pivoting (GEPP).

C++ API

void GEPPGrowth(Matrix<F> &A, Int n)

void GEPPGrowth(AbstractDistMatrix<F> &A, Int n)

C API

ElError ElGEPPGrowth_s(ElMatrix_s A, ElInt n)

ElError ElGEPPGrowth_d(ElMatrix_d A, ElInt n)

ElError ElGEPPGrowth_c(ElMatrix_c A, ElInt n)

ElError ElGEPPGrowth_z(ElMatrix_z A, ElInt n)

ElError ElGEPPGrowthDist_s(ElDistMatrix_s A, ElInt n)

ElError ElGEPPGrowthDist_d(ElDistMatrix_d A, ElInt n)

ElError ElGEPPGrowthDist_c(ElDistMatrix_c A, ElInt n)

ElError ElGEPPGrowthDist_z(ElDistMatrix_z A, ElInt n)

Python API

GEPPGrowth(A, n)