Matrix splitting

A splitting

A = M - N

with invertible

M

produces

x^{(k + 1)} = M^{- 1} N x^{(k)} + M^{- 1} b .

Table of contents
- Householder-John theorem Matrix splitting

Householder-John theorem

Let

A = M - N

be Hermitian positive definite. If

M^{*} + N

is also Hermitian positive definite, then

M

is invertible and

ρ (M^{- 1} N) < 1.

Thus the stationary iteration associated with the splitting converges from every initial vector.

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Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 1 / 39A / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 40C / a / Solution

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Matrix splitting by

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Matrix splitting, also known as matrix decomposition or matrix factorization, refers to the process of expressing a matrix as a product of two or more matrices. This technique is widely used in various fields including numerical analysis, machine learning, statistics, and dimensionality reduction.

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