A Solution Approach for Lower Hessenberg Linear Systems

An approach is developed to obtain solutions to lower Hessenberg linear systems with general entries. The approach involves developing solution vectors for an extended lower Hessenberg linear system (having an extra column and an extra introduced unknown) for each nonzero term on the right hand side. The overall solution is then found through superposition and determination of the extra introduced unknown. The approach supports parallel solution algorithms without communication between processors, since each solution vector is computed independently of the others. The number of parallel processors needed will be equal to the number of nonzero right hand side terms.