— Function: int gsl_linalg_HH_solve (gsl_matrix * A, const gsl_vector * b, gsl_vector * x)

This function solves the system A x = b directly using Householder transformations. On output the solution is stored in x and b is not modified. The matrix A is destroyed by the Householder transformations.

— Function: int gsl_linalg_HH_svx (gsl_matrix * A, gsl_vector * x)

This function solves the system A x = b in-place using Householder transformations. On input x should contain the right-hand side b, which is replaced by the solution on output. The matrix A is destroyed by the Householder transformations.