Bisection forAx=λBx with matrices of variable band width
Tóm tắt
Some extensions of the bisection method and of the inverse vector iteration for the general eigenvalue problemAx=λBx with symmetric matrices are given. A version with restricted pivoting is applied to sparse matricesA andB in which case the decomposition ofA-μB can be performed within an extended envelope with respect to the envelopeA andB. The effect of these refinements is illustrated by an example.
Tài liệu tham khảo
Bunch, J. R., Kaufman, L.: Some stable methods for calculating inertia and solving symmetric linear systems. Mathematics of Computation31, 163–179 (1977).
Parlett, B. N.: The symmetric eigenvalue problem. Englewood Cliffs, N. J.: Prentice-Hall 1980.
Schwarz, H. R.: Two algorithms for treatingAx=λBx. Comp. Meths. Appl. Mech. Eng.12, 181–199 (1977).
Schwarz, H. R.: Methode der finiten Elemente. Stuttgart: Teubner 1980.
Wilkinson, J. H.: Rundungsfehler. Berlin-Heidelberg-New York: Springer 1969.