International Journal of Difference Equations
Open Access
  • Year: 2006
  • Volume: 1
  • Issue: 1

Trigonometric Recurrence Relations and Tridiagonal Trigonometric Matrices*

  • Author:
  • Ondřej Došlý1, Šárka Pechancová2
  • Total Page Count: 11
  • Page Number: 19 to 29

1Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, CZ-662 95 Brno, Czech Republic. E-mail: dosly@math.muni.cz

2Department of Mathematics, Faculty of Civil Engineering, Brno University of Technology, Žižkova 17, CZ-602 00 Brno, Czech Republic. E-mail: pechancova.s@fce.vutbr.cz

* Research supported by the Grant 201/04/0580 of the Czech Grant Agency and the Research Project MSM0022162409 of the Czech Ministry of Education

Abstract

We show that every tridiagonal symmetric matrix can be transformed by a special transformation into the so-called tridiagonal trigonometric matrix. The relationship of this transformation to 2 × 2 trigonometric symplectic system and to three-term trigonometric recurrence relations is discussed as well.

Keywords

Threeterm recurrence relation, symplectic difference system, trigonometric transformation, trigonometric system, Sturm-Liouville difference equation