The problem of solving very large systems of linear algebraic equations appears in many real world applications such as image reconstruction, economic modeling, data mining, statistical analysis, network flows, optimization, computational mechanics, etc.

In this talk, we present a new class of accelerated algorithms, their comparison with standard methods, and will show some software which can be applied to difficult problems. The focus will be on the key algorithmic ideas aiming at the audience of computer scientists and applied mathematicians without assuming a special background in this field.