Matrix-Free-Preconditioner: Math 270C Final Project

In this project, we implemented the matrix-free preconditioner from

Stefania Bellavia, Jacek Gondzio, and Benedetta Morini. 2013. A matrix-free preconditioner for sparse symmetric positive definite systems and least-squares problems. SIAM Journal on Scientific Computing 35, 1 (2013), A192–A211

[Project Report]

Build

mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j12

An executable 'preconditioner_test' will be generated under build/bin

Run

Download system_matrix_random_F.bin from this Google Drive under data folder.

./build/bin/preconditioner_test

This demo will load the above the matrix and solve a linear system where the ground truth solution is a vector whose elements are all 1's. The LMP

Other Statistics

Plot of largest eigen value w.r.t. k

Plot of iteration number w.r.t. k