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Author Gibbs, Norman E. ♦ Poole, William G.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Graph ♦ Permutation ♦ Bandwidth ♦ Eigenvalues ♦ Sparse matrix ♦ Tridiagonal matrix ♦ Algorithm
Abstract 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.
Description Affiliation: College of William and Mary, Williamsburg, VA (Gibbs, Norman E.; Poole, William G.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 17
Issue Number 1
Page Count 5
Starting Page 20
Ending Page 24


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Source: ACM Digital Library