Quantum relaxed row and column iteration methods based on block-encoding

Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices iterative processes, which generalize to solve on a computer. Comparing with conventional methods, convergence accelerates when appropriate parameters are chosen. Once states efficiently prepared, complexity our improved exponentially number steps. In addition, phase estimations Hamiltonian simulations not required these algorithms.