Chapter 6, Problem 6.18.2E

Program Plan Intro

Sparse Matrix:

A matrix is a two-dimensional data object made of m rows and n columns, therefore having total  $m\times n$ values and a matrix which contains very few non-zero elements is called sparse matrix.

They usually lack the spatial locality in the data stream found in matrix operations.

Example of a sparse matrix:

$M=\left(\begin{array}{l}0000\\ 5800\\ 0030\\ 0600\end{array}\right)$

Here, “M” is a “$4\times 4$” sparse matrix as most of the elements are “0”.

Yale Sparse Matrix Format:

The Yale Sparse Matrix Format or the Compressed Sparse Row (CSR) is used to represent a sparse matrix by three arrays that contains non zero values.

The Yale Sparse Matrix format stores a sparse $m\times n$ matrix M in row representation using three one-dimensional arrays known as (A, IA, JA) and “NNZ” is used to denote the number of nonzero entries in matrix “M”.

“R” is used to represent the number of non-zero entries.