Abstract :

Hierarchical Matrix technique is used to approximate the data sparse dense matrix arising from the discretisation of the integral equation or the matrix arising from the elliptic partial Differential equations. It accelerates the matrix operations by performing computations involved, in an almost linear complexity.The treatment of systems of linear equations using hierarchical technique can be classified between direct method and iterative method. Hierarchical matrix technique heavily relies on the fact that sub-block of the dense matrix are low rank matrices( rank of sub block << size of sub block). In this talk we will first discuss the low rank algebra starting from the storage cost to operation counts. Then we will look into the foundations required to define the technique of hierarchical matrix and the discussion with applications of Hierarchical technique.