Moreover since the triangular matrix equations

Info icon This preview shows pages 19–20. Sign up to view the full content.

View Full Document Right Arrow Icon
mon linear matrix equations. Moreover, since the triangular matrix equations considered also appear as frequent subproblems in solving Riccati-type matrix equations, we foresee a great impact of our work in control theory applications. ACKNOWLEDGMENTS We thank Fred Gustavson and the colleagues in the Ume˚a HPC and Parallel Computing Research Group for stimulating and fruitful discussions. Finally, we thank Sven Hammarling and the referees for constructive comments on an earlier version of this manuscript. REFERENCES A NDERSON , E., B AI , Z., D EMMEL , J., D ONGARRA , J., D U C ROZ , J., G REENBAUM , A., H AMMARLING , S., M C K EN - NEY , A., O STROUCHOV , S., AND S ORENSEN , D. 1999. LAPACK Users’ Guide , third ed. SIAM, Philadel- phia. B ARTELS , R. H. AND S TEWART , G. W. 1972. Algorithm 432: Solution of the equation AX + XB = C , Commun. ACM 15 , 9, 820–826. C HU , K.-W. E. 1987. The solution of the matrix equation AXB - CXD = Y and ( YA - DZ , YC - BZ ) = ( E , F ). Linear Algebra Appl. 93 , 93–105. D ACKLAND , K. AND AGSTR ¨ OM , B. 1999. Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form. ACM Trans. Math. Softw. 25 , 4, 425–454. G ARDINER , J. D., L AUB , A. J., A MATO , J. J., AND M OLER , C. B. 1992a. Solution of the Sylvester matrix equation AXB T + CXD T = E . ACM Trans. Math. Softw. 18 , 223–231. G ARDINER , J. D., W ETTE , M. R., L AUB , A. J., A MATO , J. J., AND M OLER , C. B. 1992b. A Fortran 77 software package for solving the Sylvester matrix equation AXB T + CXD T = E . ACM Trans. Math. Softw. 18 , 232–238. G OLUB , G., N ASH , S., AND V AN L OAN , C. 1979. A Hessenberg–Schur method for the matrix problem AX + XB = C . IEEE Trans. Autom. Contr. AC-24 , 6, 909–913. H AGER , W. W. 1984. Condition estimates. SIAM J. Sci. Stat. Comp. 5 , 311–316. H AMMARLING , S. J. 1982. Numerical solution of the stable, non-negative definite Lyapunov equa- tion. IMA J. Numer. Anal. 2 , 303–323. H IGHAM , N. J. 1988. Fortran codes for estimating the one-norm of a real or complex matrix with applications to condition estimation. ACM Trans. Math. Softw. 14 , 381–396. H IGHAM , N. J. 1993. Perturbation theory and backward error for AX - X B = C . BIT 33 , 124–136. J ONSSON , I. AND AGSTR ¨ OM , B. 2001. Recursive blocked algorithms for solving triangular ma- trix equations—Part II: Two-sided and generalized Sylvester and Lyapunov equations. SLICOT ACM Transactions on Mathematical Software, Vol. 28, No. 4, December 2002.
Image of page 19

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Recursive Blocked Algorithms—Part II 435 Working Note 2001-5. Department of Computing Science, Ume˚a University, SE-901 87 Ume˚a, Sweden. J ONSSON , I. AND AGSTR ¨ OM , B. 2002. Recursive blocked algorithms for solving triangular systems— Part I: One-sided and coupled Sylvester-type matrix equations. ACM Trans. Math. Softw . 28 , 4, (Dec.). AGSTR ¨ OM , B. 1994. A perturbation analysis of the generalized Sylvester equation ( AR - LB , DR - LE ) = ( C , F ). SIAM J. Matrix Anal. Appl. 15 , 4, 1045–1060. AGSTR ¨ OM , B. AND P OROMAA , P. 1996. LAPACK–style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs.
Image of page 20
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern