The Chebyshev method is a numerical algorithm used for solving linear systems of equations. It is based on the Chebyshev polynomial, which is a mathematical expression used to approximate functions. The method iteratively improves a solution by taking advantage of properties of the Chebyshev polynomial to converge to an accurate solution efficiently. Chebyshev methods are often used in high-performance computing and scientific simulations due to their ability to efficiently solve large sparse linear systems.