ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH

Tim Hopkins; Emrah Kılıç

doi:10.11948/20210441

2022 Volume 12 Issue 6

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Tim Hopkins, Emrah Kılıç. ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2299-2313. doi: 10.11948/20210441

Citation:

Tim Hopkins, Emrah Kılıç. ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2299-2313. doi: 10.11948/20210441

ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH

Tim Hopkins¹,
Emrah Kılıç^2, ,

1.
Computing Laboratory, University of Kent, Canterbury, CT2 7NF, UK
2.
TOBB University of Economics and Technology, Mathematics Department, 06560 Ankara, Turkey

Corresponding author: Email: ekilic@etu.edu.tr (E. Kılıç)

Abstract

Abstract

We present a fast algorithm for generating the inverse and the determinant of an extended, periodic, tridiagonal matrix. We use backward continued fractions to generate the elements of the inverse in closed form. By trading memory use against the cost of repeating the computation of certain quantities we are able to produce an effective procedure for a symbolic algebra implementation. We compare the performance of our Maple implementation with that of the standard Maple library procedures for matrix inversion and computation of the determinant on a set of illustrative example matrices.
- Matrix inversion /
- LU-Factorization /
- backward continued fraction /
- almost periodic tridiagonal matrix
MSC: 15A09

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References

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