A
system of linear equations consists of a known
matrix and a known
vector. To solve the system is to find the value of the unknown vector .[3][5] A direct method for solving a system of linear equations is to take the inverse of the matrix , then calculate . However, computing the inverse is computationally expensive. Hence, iterative methods are commonly used. Iterative methods begin with a guess , and on each iteration the guess is improved. Once the difference between successive guesses is sufficiently small, the method has converged to a solution.[6][7]
^
abHenk van der Vorst (2003). "Bi-Conjugate Gradients". Iterative Krylov Methods for Large Linear Systems. Cambridge University Press.
ISBN0-521-81828-1.
^"Linear equations"(PDF), Matrix Analysis and Applied Linear Algebra, Philadelphia, PA: SIAM, pp. 1–40,
doi:
10.1137/1.9780898719512.ch1 (inactive 31 January 2024), archived from
the original(PDF) on 2004-06-10, retrieved 2023-12-18{{
citation}}: CS1 maint: DOI inactive as of January 2024 (
link)