Startseite Mathematik A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
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A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity

  • Emrah Kiliç EMAIL logo und Didem Ersanli
Veröffentlicht/Copyright: 24. Juni 2024
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 74 Heft 3

Abstract

Filbert and Lilbert matrices are defined by terms of linear Fibonacci-like sequences. By considering terms of such linear recurrences and additional free parameters, we define a nonlinear variant of these matrices via ratios of q-forms of terms of Fibonacci-like sequences whose indices are in nonlinear forms. We derive explicit formulae for the matrices L and U come from LU-decomposition, their inverses, inverse of the main matrices and their determinants.

MSC 2010: 11B39; 05A30; 15A36; 15A15; 15A23
Keywords: Filbert matrix; Lilbert matrix; q-analogue; LU-decomposition; inverse matrix; determinant

  1. Communicated by István Gaál

References

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Received: 2023-05-04
Accepted: 2023-09-19
Published Online: 2024-06-24
Published in Print: 2024-06-25

© 2024 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. On the Paley graph of a quadratic character
  2. A topological duality for tense modal pseudocomplemented De Morgan algebras
  3. Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
  4. A general formula in composition theory
  5. A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
  6. On universality in short intervals for zeta-functions of certain cusp forms
  7. On asymptotics for lacunary partition functions
  8. Parallel surfaces of the non-lightlike solution of vortex filament equations
  9. New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
  10. Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
  11. Approximation theorems via Pp-statistical convergence on weighted spaces
  12. Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
  13. Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
  14. On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
  15. Positive bases, cones, Helly-type theorems
  16. Digital Jordan surfaces arising from tetrahedral tiling
  17. Influence of ideals in compactifications
  18. On the functions ωf and Ωf
  19. On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
  20. A bivariate distribution with generalized exponential conditionals
  21. A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
https://doi.org/10.1515/ms-2024-0044
Schlagwörter für diesen Artikel
Filbert matrix; Lilbert matrix; q-analogue; LU-decomposition; inverse matrix; determinant

Artikel in diesem Heft

  1. On the Paley graph of a quadratic character
  2. A topological duality for tense modal pseudocomplemented De Morgan algebras
  3. Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
  4. A general formula in composition theory
  5. A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
  6. On universality in short intervals for zeta-functions of certain cusp forms
  7. On asymptotics for lacunary partition functions
  8. Parallel surfaces of the non-lightlike solution of vortex filament equations
  9. New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
  10. Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
  11. Approximation theorems via Pp-statistical convergence on weighted spaces
  12. Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
  13. Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
  14. On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
  15. Positive bases, cones, Helly-type theorems
  16. Digital Jordan surfaces arising from tetrahedral tiling
  17. Influence of ideals in compactifications
  18. On the functions ωf and Ωf
  19. On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
  20. A bivariate distribution with generalized exponential conditionals
  21. A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
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