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Nonnegative matrices with prescribed extremal singular values

✍ Scribed by Emedin Montaño; Mario Salas; Ricardo L. Soto

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
295 KB
Volume
56
Category
Article
ISSN
0898-1221

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✦ Synopsis

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n -1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n × n nonnegative bidiagonal matrix B and an n × n nonnegative semi-bordered diagonal matrix C, such that σ ( j) 1 and σ ( j) j are, respectively, the minimal and the maximal singular values of certain submatrices B j and C j of B and C, respectively. By using a singular value perturbation result, we also construct an n × n nonnegative matrix with prescribed singular values σ 1 ≥ • • • ≥ σ n .

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