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Symbolic calculation of the trace of the power of a tridiagonal matrix

Symbolische Berechnung der Spur einer Potenz einer Tridiagonalmatrix

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Abstract

An algorithm symbolically calculating the trace of the power of a tridiagonal matrix is proposed. The setting is based on techniques developed from structure analysis and combinatorics. The complexity analysis, the extension and the possible applications of this algorithm are also discussed.

Zusammenfassung

Es wird ein Algorithmus vorgeschlagen, der die Spur einer Potenz einer Tridiagonalmatrix berechnet. Er stützt sich auf Techniken, die aus der Strukturanalysis und der Kombinatorik stammen. Die Komplexität des Algorithmus wird analysiert, Verallgemeinerungen und mögliche Anwendungen werden diskutiert.

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References

  1. Capel, H. W., Tindemans, P. A. J.: An inequality for the trace of matrix products Rep. Mathematical Phys.6, 225–235 (1974).

    Article  Google Scholar 

  2. Datta, B. N., Datta, K.: An algorithm for computing powers of a Hessenberg matrix and its applications. Linear Alg. Appl.14, 273–284 (1976).

    Article  Google Scholar 

  3. Davis, C.: An inequality for traces of matrix functions. Czechoslavak Math. J.15, 37–41 (1965).

    Google Scholar 

  4. Harary, T., Palmer, E.: Graphical Enumeration. New York: Academic Press 1973.

    Google Scholar 

  5. Khati, C. G.: Powers of matrices and idempotency. Linear Alg. Appl.33, 57–65 (1980).

    Article  Google Scholar 

  6. Kristof, W.: A theorem on the trace of certain matrix products J. Math. Psychol.7, 515–530 (1970).

    Article  Google Scholar 

  7. Leron, U.: Trace identities and polynomial identifies ofn×n matrices J. Alg.42, 369–377 (1976).

    Article  Google Scholar 

  8. Mirsky, L.: On the trace of matrix products. Math. Nachr.20, 171–174 (1959).

    Google Scholar 

  9. Pugacev, V. P.: Application of the trace of a matrix to the evaluation of its proper values. Z. Vychisl. Mat. i Mat. Fiz.5, 114–116 (1965).

    Google Scholar 

  10. Rothblum, U. G.: Expansions of sums of matrix powers. SIAM Review23, 143–164 (1981).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 27695-8205, Raleigh, NC, U.S.A.

    M. T. Chu

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  1. M. T. Chu
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Chu, M.T. Symbolic calculation of the trace of the power of a tridiagonal matrix. Computing 35, 257–268 (1985). https://doi.org/10.1007/BF02240193

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  • DOI: https://doi.org/10.1007/BF02240193

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