The algebraic eigenvalue problem
The algebraic eigenvalue problem
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The profile of the Cartesian product of graphs
Discrete Applied Mathematics
| Hi-index | 48.22 |
Tridiagonalizing a matrix by similarity transformations is an important computational tool in numerical linear algebra. Consider the class of sparse matrices which can be tridiagonalized using only row and corresponding column permutations. The advantages of using such a transformation include the absence of round-off errors and improved computation time when compared with standard transformations. A graph-theoretic algorithm which examines an arbitrary n × n matrix and determines whether or not it can be permuted into tridiagonal form is given. The algorithm requires no arithmetic while the number of comparisons, the number of assignments, and the number of increments are linear in n. This compares very favorably with standard transformation methods. If the matrix is permutable into tridiagonal form, the algorithm gives the explicit tridiagonal form. Otherwise, early rejection will occur.