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Solution of the Inverse Problem for the Two-Dimensional Discrete Schrödinger Equation Using REDUCE

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Abstract

Actual calculations carried out on SPP with the use of the REDUCE system made it possible to completely clarify the statement of the inverse problem for the two-dimensional discrete Schrödinger equation. The corresponding symmetric pentadiagonal matrix can be reconstructed from the given spectrum and first k components for all basis eigenvectors. A simple formula is obtained to determine k. The developed algorithm for solving the inverse problem is unstable. Newton iterations do not always converge.

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REFERENCES

  1. Serdyukova, S.I., Solving Large Systems of Polynomial Equations Using REDUCE, Programmirovanie, 2000, no. 1, pp. 41-43.

  2. Serdyukova, S.I., Inverse Problem for Symmetric Tridiagonal Matrices. Calculation of the System of Discrete Orthogonal Polynomials with Arbitrary Weight, Russ. J. Numer. Anal. Math. Modeling, 1993, vol. 8, no. 3, pp. 245-263.

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  3. Hearn, A.C., REDUCE User's Manual, Version 3.6, Santa Monica, CA, 1995.

  4. Serdyukova, S.I., Inverse Problem for the Two-Dimensional Discrete Schrödinger Equation, Preprint of Joint Inst. for Nuclear Res., Dubna, 2000, no. P11-2000-57.

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  1. Computer Technologies and Automation Laboratory, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    S. I. Serdyukova

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  1. S. I. Serdyukova
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Serdyukova, S.I. Solution of the Inverse Problem for the Two-Dimensional Discrete Schrödinger Equation Using REDUCE. Programming and Computer Software 27, 4–5 (2001). https://doi.org/10.1023/A:1007122416559

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  • DOI: https://doi.org/10.1023/A:1007122416559

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