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Fiedler, Miroslav
A deflation formula for tridiagonal matrices. (English). Aplikace matematiky, vol. 25 (1980), issue 5, pp. 348-357
MSC: 15A18, 65F15 | MR 0590488 | Zbl 0456.65018 | DOI: 10.21136/AM.1980.103869
Keywords:
deflation formula; tridiagonal matrices
Summary:
An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.
References:
[1] J. H. Wilkinson: The algebraic eigenvalue problem. Clarendon Press, Oxford 1965. MR 0184422 | Zbl 0258.65037
[2] P. A. Businger: Numerically stable deflation of Hessenberg and symmetric tridiagonal matrices. BIT 11 (1971), 262-270. DOI 10.1007/BF01931807 | MR 0293828 | Zbl 0226.65028
[3] W. Gander: Stationärer Quotienten-Differenzen Algorithmus. Prozedur qdstat. In: Numerische Prozeduren aus Nachlass und Lehre von Prof. Heinz Rutishauser. ISNM Vol. 33. Birkhäuser Verlag 1977. MR 0488607 | Zbl 0358.65033
[4] W. Jentzsch: Über Integralgleichungen mit positivem Kern. J. für Math. 141 (1912), 235 - 244.
[5] M. Fiedler, Vl. Pták: On matrices with non-positive off-diagonal elements and positive principal minors. Czech. Math. J. 87 (1962), 382 - 400. MR 0142565
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