A new family of companion forms of polynomial matrices
In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is…
A new kind of companion matrix
A new kind of companion matrix is introduced, for polynomials of the form c(I») = I»a(I»)b(I»)+c_0, where upper Hessenberg companions are known for the polynomials a(I») and b(I»). This construction…
A FACTORIZATION OF THE INVERSE OF THE SHIFTED COMPANION MATRIX
- Computer Science, Mathematics
A method for factoring the shifted companion matrix CI is presented and the cost of multiplying a vector by (CI) 1 is shown to be O(n), and therefore, any shift and invert eigenvalue method can be implemented efficiently.
2 Characterization of Matrices in H n with a Pentadiagonal Form
- Computer Science
This work determines which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix and describes how to find the permutation involved.
SHOWING 1-5 OF 5 REFERENCES
Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices
- MathematicsStatistical Inference for Engineers and Data Scientists
This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.
- Linear Algebra Appl