In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i -th …

Jun 12, 2025 · This guide provides a comprehensive overview of iterative methods in numerical analysis, including their definition, importance, and history. We will cover the different types of iterative …

In numerical analysis, iteration is a technique used to tackle mathematical problems, including algebraic equations, differential equations, optimization, and many others.

For a given equation f(x) = 0, find a fixed point function which satisfies the conditions of the Fixed-Point Theorem (also nice if the method converges faster than linearly).

Gauss–Seidel method. We take A B = L0 + D = L, the lower-triangular part of A, and we generate the sequence (x(k)) by solving the triangular system

Instead of using O(m3) operations to find a solution using direct methods, in many cases it is possible to find a good approximation (maybe even indistinguishable from the “correct” solution in a floating …

We are turning from elimination to look at iterative methods. There are really two big decisions, the preconditioner P and the choice of the method itself: A good preconditioner P is close to A but much …