This chapter discusses the recognition of TN matrices. It touches on one of the many applications for the structure of TN matrices. TN matrices enjoy tremendous structure, as a result of requiring all minors to be nonnegative. This intricate structure makes it easier to determine when a matrix is TP than to check when it is a P-matrix, which formally involves far fewer minors. Vandermonde matrices arise in the problem of determining a polynomial of degree at most n − 1 that interpolates n data points. Suppose that n data points (xᵢ,yᵢ)unconverted formula are given. The goal is to construct a polynomial p(x) = a₀ + a₁x + … + asubscript n − 1xsuperscript n − 1 that satisfies p(xᵢ) = yᵢ for i = 1, 2, …,n.
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