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Balancing is then based on equilibrating row and column norms of the Hamiltonian matrix using symplectic scaling matrices. Due to the given structure, it is sufficient to deal with the leading half rows and columns of the matrix. Numerical examples show that the method improves eigenvalue calculations of Hamiltonian matrices as well as numerical methods for solving continuous-time algebraic Riccati equations.<\/jats:p>","DOI":"10.1137\/s1064827500367993","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1885-1904","source":"Crossref","is-referenced-by-count":18,"title":["Symplectic Balancing of Hamiltonian Matrices"],"prefix":"10.1137","volume":"22","author":[{"given":"Peter","family":"Benner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","first-page":"0","volume":"1","author":"Ammar Gregory","year":"1993","journal-title":"Electron. Trans. Numer. Anal."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90325-Q"},{"key":"R3","unstructured":"E. Anderson, Z. Bai, C. Bischof, S. 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