Superhigh-Speed Iterative Solvers of Linear Matrix

Publication type Article
Status Published
Affiliation: Bauman Moscow State Technical University
Address: Russian Federation
Affiliation: Bauman Moscow State Technical University
Address: Russian Federation
Affiliation: Bauman Moscow State Technical University
Address: Russian Federation
Affiliation: Bauman Moscow State Technical University
Address: Russian Federation
Journal nameDoklady Akademii nauk
EditionVolume 482 Issue 3


Publication date08.11.2018
Cite   Download pdf To download PDF you should sign in
Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

views: 1266

Readers community rating: votes 0

1. Helmke U., Jordan J. Control and Stabilization of Linear Equation Solv-ers // Lecture Notes in Control and Information Sciences. Springer-Verlag Berlin, 2010. P. 73 – 82.

2. Helmke U., Jordan J. Optimal control of iterative solution methods for linear systems of equations // Proc. Appl. Math. Mech. 2005. Vol. 5(1). P. 163 – 164.

3. Embree M. The tortoise and the hare restart GMRES // SIAM Review. 2003. Vol. 45. P. 259 – 266.

4. Zubov N.E., Mikrin E.A., Ryabchenko V.N. Matrichnye metody v teo-rii i praktike sistem avtomaticheskogo upravleniya letatel'nymi apparatami. M.: Izd-vo MGTU imeni N.Eh. Baumana, 2016.

5. Bellman R.E. Introduction to the Mathematical Theory of Control Pro-cesses // Nonlinear processes. 1971. Vol. II. Academic Press, New York.

6. Gustafsson K., Lundh M., Soderlind G.S. A PI stepsize control for the numerical solution of ordinary differential equations // BIT. 1988. Vol. 28 P. 270 – 287.

7. Gustafsson K. Control theoretic techniques for stepsize selection in ex-plicit Runge-Kutta methods // ACM Trans. Math. Softw. 1991. Vol. 17(4). P. 533 – 554.

8. Helmke U., Fuhrmann P.A. Controllability of matrix eigenvalue algo-rithms: the inverse power method // Systems & Control Letters. 2000. Vol. 41. P. 57 – 66.

9. Helmke U., Jordan J., Lanzon A. A control theory approach to linear equation solvers // Proc. of 17th International Symposium on Mathemat-ical Theory of Network and Systems (MTNS), 2006. Kyoto, Japan.

10. Helmke U., Wirth F. On controllability of the real shifted inverse power iteration // Systems & Control Letters. 2001. Vol. 43. P. 9 – 23.

11. Bhaya A., Kaszkurewicz E. Control Perspectives on Numerical Al-gorithms and Matrix Problems // Advances in Design and Control. 2006. Vol. 10. SIAM, Philadelphia.

12. Kashima K., Yamamoto Y. System theory for numerical analysis // Automatic. 2007. Vol. 43(7). P. 1156 – 1164.

13. Wakasa Y., Yamamoto Y. An iterative method for solving linear equations by using robust methods // Proc. of SICE first Annual Confer-ence on Control Systems. 2001. P. 451 – 454.

14. Polyak B.T., Scherbakov P.S. Robastnaya ustojchivost' i upravle-nie. M.: Nauka, 2002.

15. Girko V.L. Circular Law // Theory Probab. Appl., 1984, No. 29, P. 694 – 706.

Система Orphus