---
title: Iterative Methods
description: Iterative methods generate sequences of approximations to solve complex mathematical problems, particularly large linear systems. Learners will understand convergence criteria, error bounds, and how to implement these algorithms for computational efficiency.
category: mathematics
subcategory: numerical-linear-algebra
difficulty: beginner, intermediate, advanced
url: /subject/iterative-methods
---

# Iterative Methods

Iterative methods generate sequences of approximations to solve complex mathematical problems, particularly large linear systems. Learners will understand convergence criteria, error bounds, and how to implement these algorithms for computational efficiency.

## Available Resources

1 Books • 1 Courses • 2 Websites

## Websites

### 1. PETSc Documentation

Reference manual for KSP, the Krylov subspace solver interface in the PETSc scientific computing library. Documents GMRES, conjugate gradient, BiCGStab, MINRES and other solvers, plus preconditioner pairing, convergence tests, and monitors used to solve large sparse linear systems in parallel code.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://petsc.org/release/docs/manualpages/KSP/index.html

**Tags:** krylov-subspace-methods, petsc, sparse-linear-systems, preconditioning, parallel-computing

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Scientific Computing

Learn iterative methods in scientific computing with this course by Nick Trefethen. Master numerical techniques for solving complex problems!

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.maths.ox.ac.uk/node/34949

## Books

### 1. Iterative Methods for Sparse Linear Systems

**Author:** Yousef Saad

Standard SIAM graduate text on solving large sparse linear systems iteratively. Covers sparse storage formats, classical relaxation, projection and Krylov subspace methods such as GMRES and conjugate gradient, preconditioning techniques including incomplete factorizations, multigrid, domain decomposition, and their parallel implementation.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0898715342?tag=edmonddante07-20

**Tags:** krylov-subspace-methods, sparse-linear-systems, preconditioning, numerical-linear-algebra, gmres

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