Rounding errors in solving block Hessenberg systems

Rounding errors in solving block Hessenberg systems

A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.

Implementing an Algorithm for Solving Block Hessenberg Systems Implementing an Algorithm for Solving Block Hessenberg Systems

This paper describes the implementation of a recursive descent method for solving block Hessenberg systems. Although the algorithm is conceptually simple, its implementation in C (a natural choice of language given the recursive nature of the algorithm and its data) is nontrivial. Particularly important is the balance between ease of use, computational eeciency, and exibility. This report and t...

Parallel Reduction from Block Hessenberg to Hessenberg using MPI

In many scientific applications, eigenvalues of a matrix have to be computed. By first reducing a matrix from fully dense to Hessenberg form, eigenvalue computations with the QR algorithm become more efficient. Previous work on shared memory architectures has shown that the Hessenberg reduction is in some cases most efficient when performed in two stages: First reduce the matrix to block Hessen...

Rounding errors in algebraic processes

Rounding Errors and Volatility Estimation

Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the asymptotic behavior of the Realized Volatility (RV), which is commonly used as an estimator of the...