A Study on Algebra for Real Life Approach

In practically every area of mathematics, linear algebraic systems are crucial. In the case of table-top numerical experiments, such systems may very well be resolved using well-known techniques like LU decomposition, but in a large range of situations, the size of the matrices would make them unstorable even given the ample storage space currently available. However, the matrices in these situations typically have a highly sparse structure, greatly lowering their memory footprint. The disadvantage is that an inverse of a sparse matrix is typically dense, making LU decomposition an impractical method. In these situations, iterative methods are used to solve the linear system by virtue of a fixed-point iteration, such as generalised minimal residues iteration and bi-conjugate gradient stabilised iteration.