@inbook{fdb20567866245eebed65686594e75c4,
title = "Efficient transformation for block-diagonalization",
abstract = "Use of block-diagonalization of the Jacobian matrix in bifurcation analysis of symmetric systems was demonstrated in Chap. 12. By taking advantage of the underlying geometrical structure of dihedral group symmetry, we give a systematic procedure to determine the transformation matrix for block-diagonalization and an efficient method to compute the block-diagonal form. Group representation theory in Chap. 7, theory of block-diagonalization in Chap. 8, and the application of these theories to the dihedral group in Chap. 9 form a foundation of this chapter.",
keywords = "Block-diagonalization, Computational efficiency, Dihedral group, Jacobian matrix, Orbit, Symmetry, Transformation matrix, Truss structure",
author = "Kiyohiro Ikeda and Kazuo Murota",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-21473-9_13",
language = "English",
series = "Applied Mathematical Sciences (Switzerland)",
publisher = "Springer",
pages = "361--402",
booktitle = "Applied Mathematical Sciences (Switzerland)",
}