Algorithms For Block Cinque-diagonal Linear Equations

Many important problems in engineering and applied sciences ultimately can be reduced to matrix computation problems.Moreover,various applications often introduce a special structure into the corresponding matrices.Among classical examples are Toeplitz matrices[a_i-j],Vandermonde matrices[a_i^j-1],Cauchy matirces[1/(a_i-b_j) and others.To achieving a fast and stable algorithm for these matrices with special or characteristic structure is an important issue in many applied areas.Thus,it is not surprising that in recent years the design of fast algorithms for structured matrices has become an increasingly important activity in a diverse variety of branches of the exact sciences.In this paper,we mainly discuss some properties and design a fast algorithm,a iterative algorithm and a parallel algorithm for block cinque-diagonal linear systems. Moreover,some practical applications of these algorithms are given.In chapter 1,we give a brief introduction to the importance and the current research situation and classical research methods on structured matrices.In chapter 2,we derive a fast algorithm for cinque-diagonal linear systems and give some practical applications.In chapter 3,we derive a iterative algorithm for cinque-diagonal linear systems and also give some practical applications.In chapter 4,we derive parallel algorithms for cinque-diagonal linear systems.