  A type of iterative orthogonally accumulated projection methods for solving
linear system of equations are proposed in this paper. This type of methods are
applications of accumulated projection(AP) technique proposed recently by
authors. Instead of searching projections in a sequence of subspaces as done in
the original AP approach, these methods try to efficiently construct a sequence
of orthonormal vectors while the inner-product between the solution to the
system and each vector in the sequence can be easily calculated, thus the
solution can be retrieved in finite number of iterations in case of exact
arithmetic operations. We also discuss the strategies to handle
loss-of-orthogonality during the process of constructing orthonormal vectors.
Numerical experiments are provided to demonstrate the efficiency of these
methods.
