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A new recursive algorithm for inverting general tridiagonal and anti-tridiagonal matrices. (English) Zbl 1157.65338
Summary: The authors present a new recursive symbolic computational algorithm for inverting general tridiagonal and anti-tridiagonal matrices. An illustrative example is given.

65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)
68W30Symbolic computation and algebraic computation
Full Text: DOI
[1] Hadj, A. Driss Aiat; Elouafi, M.: A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix. Appl. math. Comput. (2008)
[2] Burden, R. L.; Faires, J. D.: Numerical analysis. (2001) · Zbl 0671.65001
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[6] Huang, Y.; Mccoll, W. F.: Analytic inversion of general tridiagonal matrices. J. phys. A 30, 7919-7933 (1997) · Zbl 0927.15003
[7] Kilic, E.: Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions. Appl. math. Comput. 197, 345-357 (2008) · Zbl 1151.65021
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[9] Mallik, R. K.: The inverse of a tridiagonal matrix. Linear algebra appl. 325, 109-139 (2001) · Zbl 0980.15004
[10] Yamamoto, T.: Inversion formulas for tridiagonal matrices with applications to boundary value problems. Numer. funct. Anal. optimiz. 22, 357-385 (2001) · Zbl 0996.15006