{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:46:36Z","timestamp":1759837596990},"reference-count":15,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We present a real symmetric tridiagonal matrix of order<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>whose eigenvalues are<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mn>2<\/mml:mn><mml:mi>k<\/mml:mi><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mn>2<\/mml:mn><mml:mi>l<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:mrow><mml:mrow><mml:mi>l<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>. The matrix entries are explicit functions of the size<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>, 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.<\/jats:p>","DOI":"10.1155\/2014\/515082","type":"journal-article","created":{"date-parts":[[2014,5,26]],"date-time":"2014-05-26T17:04:15Z","timestamp":1401123855000},"page":"1-6","source":"Crossref","is-referenced-by-count":9,"title":["A Test Matrix for an Inverse Eigenvalue Problem"],"prefix":"10.1155","volume":"2014","author":[{"given":"G. M. L.","family":"Gladwell","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. 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