Linear problem Ax=b is considered where x is unknown and where A is
a block-tridiagonal N-dimensional matrix with all of its
off-diagonal submatrices equal to the same negative unit matrix and
with the same diagonal submatrix element C only replaced by the unit
submatrix in the upper and lower corner of A. A two-step algorithm
is proposed for the numerical solution of the system reducing the
procedure to the usual conjugate-gradient method.

MR2524047 Monastyrnyi, P. I.; Kremen', E. V.; Kremen', Yu. A.
Numerical solution of three-point difference equations on the basis
of a combination of the reduction method and the conjugate gradient
method. (Russian) Vestsi Nats. Akad. Navuk Belarusi Ser. Fiz.-Mat.
Navuk 2008, no. 1, 41--44, 126. 65Q05