Cholesky decomposition

About

In this project, the Cholesky row decomposition method was implemented for solving the following linear systems:

• A₁x = b₁
• A₂x = b₂

where A₁, A₂ ∈ ℝ^n,n and b₁, b₂ ∈ ℝⁿ:

In the context of this exercise, single-precision floating-point arithmetic was used in order to compare the two linear systems in terms of precision, as n takes value in {100, 1000, 10000}.

The purpose of this project was also to achieve the minimum time complexity for this specific form of input matrices A₁, A₂, b₁ and b₂, taking into account that A₁ and A₂ are pentadiagonal matrices.

Implementation details

The project was implemented in both Octave and C language.

The C language version supports:

• single and double-precision floating-point arithmetic by typedefing each time fptype to double or float
• optimal and non-optimal versions by defining or not preprocessor macro OPTIMIZED (see Makefile).