A Test Matrix for an Inverse Eigenvalue Problem
We present a real symmetric tridiagonal matrix of order n whose eigenvalues are {2k}k=0n-1 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l+1}l=0n-2. The matrix entries are explicit functions of the size n, and so the matrix...
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Hindawi Limited
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/515082 |
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doaj-e0dc44a5ee8d4798a35ff7f86dce13fb2020-11-24T23:37:27ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/515082515082A Test Matrix for an Inverse Eigenvalue ProblemG. M. L. Gladwell0T. H. Jones1N. B. Willms2Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, CanadaDepartment of Mathematics, Bishop’s University, Sherbrooke, QC, J1M 2H2, CanadaDepartment of Mathematics, Bishop’s University, Sherbrooke, QC, J1M 2H2, CanadaWe present a real symmetric tridiagonal matrix of order n whose eigenvalues are {2k}k=0n-1 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l+1}l=0n-2. The matrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided.http://dx.doi.org/10.1155/2014/515082 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
G. M. L. Gladwell T. H. Jones N. B. Willms |
| spellingShingle |
G. M. L. Gladwell T. H. Jones N. B. Willms A Test Matrix for an Inverse Eigenvalue Problem Journal of Applied Mathematics |
| author_facet |
G. M. L. Gladwell T. H. Jones N. B. Willms |
| author_sort |
G. M. L. Gladwell |
| title |
A Test Matrix for an Inverse Eigenvalue Problem |
| title_short |
A Test Matrix for an Inverse Eigenvalue Problem |
| title_full |
A Test Matrix for an Inverse Eigenvalue Problem |
| title_fullStr |
A Test Matrix for an Inverse Eigenvalue Problem |
| title_full_unstemmed |
A Test Matrix for an Inverse Eigenvalue Problem |
| title_sort |
test matrix for an inverse eigenvalue problem |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2014-01-01 |
| description |
We present a real symmetric tridiagonal matrix of order n whose eigenvalues are {2k}k=0n-1 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l+1}l=0n-2. The matrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided. |
| url |
http://dx.doi.org/10.1155/2014/515082 |
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