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Explicit inverses of Toeplitz and associated matrices. (English) Zbl 1116.15300
Summary: We discuss Toeplitz and associated matrices which have simple explicit expressions for their inverses. We first review existing results and generalize these where possible, including matrices with hyperbolic and trigonometric elements. In §2 we discuss and generalize the Fiedler matrix. In §3 we give an analytic procedure for inverting any band Toeplitz matrix, in §4 we invert a tridiagonal Toeplitz matrix with modified corner elements.

MSC:
15A09 Theory of matrix inversion and generalized inverses
15A06 Linear equations (linear algebraic aspects)
15B57 Hermitian, skew-Hermitian, and related matrices
Keywords:
Toeplitz matrix
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