Padé and Gregory error estimates for the logarithm of block triangular matrices

• Author(s): Cardoso, João R. ; Silva Leite, F.
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/4619
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Matrix logarithm; Inverse scaling and squaring; Padé approximants and Gregory's series
• Document Type: Article
• Language: English

Description

In this paper we give bounds for the error arising in the approximation of the logarithm of a block triangular matrix T by Padé approximants of the function f(x)=log[(1+x)/(1-x)] and partial sums of Gregory's series. These bounds show that if the norm of all diagonal blocks of the Cayley-transform B=(T-I)(T+I)-1 is sufficiently close to zero, then both approximation methods are accurate. This will contribute for reducing the number of successive square roots of T needed in the inverse scaling and squaring procedure for the matrix logarithm. http://www.sciencedirect.com/science/article/B6TYD-4G5BJ9P-2/1/398a212a906943d2474a2cd6166c1d31