A method for computing orthogonal URV/ULV decompositions of block tridiagonal (or banded) matrices is presented. The method discussed transforms the matrix into structured triangular form and has several attractive properties: The block tridiagonal structure is fully exploited; high data locality is achieved, which is important for high efficiency on modern computer systems; very little fill-in...

We describe a parallel algorithm for finding the eigenvalues and eigenvectors of a dense symmetric matrix. We follow the traditional three step process: we reduce the dense matrix to tridiagonal form, solve the tridiagonal problem then backtransform the result. Since the different steps have different algorithmic characteristics, this problem serves as an perfect vehicle for exploring some issu...

This paper proposes a method to simulate inextensible hair strands using tridiagonal matrix formulation in which distance constraints are formulated as a linear system. The proposed method avoids constructing a full matrix explicitly. Instead, it takes advantage of the chain topology and serial indexing to formulate symmetric tridiagonal matrix. Furthermore, we use a linear distance constraint ...

Abstract. We analyze the residuals of GMRES [9], when the method is applied to tridiagonal Toeplitz matrices. We first derive formulas for the residuals as well as their norms when GMRES is applied to scaled Jordan blocks. This problem has been studied previously by Ipsen [5], Eiermann and Ernst [2], but we formulate and prove our results in a different way. We then extend the (lower) bidiagona...