Abstract

1 1 Introduction 1 2 Block Representations for Representing Products of Householder Matrices 1 3 Block Schemes for Reducing a General Matrix to Hessenberg Form 2 4 Discussion of the Various Update Schemes 4 References 6 ii A Summary of Block Schemes for Reducing a General Matrix to Hessenberg Form by Christian H. Bischof Abstract. Various strategies have been proposed for arriving at block algorithms for reducing a general matrix to Hessenberg form by means of orthogonal similarity transformations. This paper reviews and systematically categorizes the various strategies and discusses their computational characteristics. 1 Introduction Let A be an n \Theta n symmetric matrix. Our goal is to compute an orthogonal matrix Q, Q T Q = I such that Q T AQ = H where H is of upper Hessenberg form. The standard algorithm [10] reduces A one column at a time through Householder transformation at a cost of O(4=3n 3 ) flops. It mainly employs matrix-vector multiplications and symmetric r...

Citations