In this chapter, I am trying to prove, that the multi-frontal solvers that are built based on the metho-

dology presented in this book are fast. But what does it mean to have a faster solver, and how can

we compare our new solver with other state-of-the-art solvers, e.g., MUMPS [63] solver? The first

question to answer is ‘’How are we going to compare our solver?”. What measure are we going to

use, and what is the meaning of this measure? I propose the following three measures:

1. Execution time

2. Number of Floating Point Operations (FLOPs)

3. Efficiency and speedup for parallel execution

There may be many other measures utilized for comparison of multi-frontal direct solvers, like me-

mory usage, amount of data transferred during the communication, and many more. All these me-

asures are very important and cannot be neglected; however, I believe these three above mentioned

measures are the most important. Many scientific authors compare numerical algorithms including

solvers but do not provide all the necessary details, they are not aware of the real reason why their

algorithm is faster (or slower) than the other one.