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In this paper, we propose and discuss a class of inverse eigenvalue problems for real symmetric banded matrices with odd bandwidth. For an odd 2p+1 with a positive integer p, the problem is to construct an n×n real symmetric banded matrix with bandwidth 2p+1 whose m×m leading principal submatrix is a given m×m real symmetric banded matrix with bandwidth 2p+1 and spectrum is a given set of real numbers...
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