Construct an orthogonal basis u of block Krylov subspace
[v a*v a^2*v ... a^(k+1)*v]Using Householder reflections to guard against loss of orthogonality.
If v is a vector, then h contains the Hessenberg matrix such that
a*u == u*h+rk*ek'
, in whichrk = a*u(:,k)-u*h(:,k)
, andek'
is the vector[0, 0, ..., 1]
of lengthk
. Otherwise, h is meaningless.If v is a vector and k is greater than
length(A)-1
, then h contains the Hessenberg matrix such thata*u == u*h
.The value of nu is the dimension of the span of the krylov subspace (based on eps1).
If b is a vector and k is greater than m-1, then h contains the Hessenberg decomposition of a.
The optional parameter eps1 is the threshold for zero. The default value is 1e-12.
If the optional parameter pflg is nonzero, row pivoting is used to improve numerical behavior. The default value is 0.
Reference: Hodel and Misra, "Partial Pivoting in the Computation of Krylov Subspaces", to be submitted to Linear Algebra and its Applications