psfun_d_arnoldi Interface

interface

Simple polynomial method based on the Arnoldi orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

public module subroutine psfun_d_arnoldi(fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Arguments

Type	Intent	Optional	Attributes		Name
type(psfun_d_serial),	intent(inout)			::	fun	Function object
type(psb_dspmat_type),	intent(in)			::	a	Distribute sparse matrix
type(psb_desc_type),	intent(in)			::	desc_a	Descriptor for the sparse matrix
type(psb_d_vect_type),	intent(inout)			::	y	Output vector
type(psb_d_vect_type),	intent(inout)			::	x	Input vector
real(kind=psb_dpk_),	intent(in)			::	eps	Requested tolerance
integer(kind=psb_ipk_),	intent(out)			::	info	Output flag
integer(kind=psb_ipk_),	intent(in),	optional		::	itmax	Maximum number of iteration
integer(kind=psb_ipk_),	intent(in),	optional		::	itrace	Trace for logoutput
integer(kind=psb_ipk_),	intent(in),	optional		::	istop	Stop criterion
integer(kind=psb_ipk_),	intent(out),	optional		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(out),	optional		::	err	Last estimate error
real(kind=psb_dpk_),	intent(out),	optional	allocatable	::	res(:)	Vector of the residuals

Description

Simple polynomial method based on the Arnoldi orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

$$\begin{equation*} \mathcal{K}_k(A,x) = \{x,Ax,\ldots,A^{k-1}x\}, \end{equation*}$$

and approximates $y = f(\alpha A)x \approx \beta_1 V_k f(H_k) e_1$,for $\beta_1 = \|x\|_2$, $e_1$ the first vector of the canonical base of $\mathbb{R}^k$, and $H_k$ the Hessemberg matrix given by $H_k = V_k^T A V_k$.