Bounded solutions of quadratic circulant difference equations

Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers

“…It is important to develop new theories and methods and to modify and refine the well-known techniques, for solving differential equations. On the basis of existing application situation [1][2][3][4][5][6][7][8][9][10][11], we will exploit solving some differential equations based on the RSFPLR circulant matrices and RSLPFL circulant matrices.…”

“…By using a Strang-type block-circulant preconditioner, Zhang et al [3] speeded up the convergent rate of boundary-value methods. Delgado et al [4] developed some techniques to obtain global hyperbolicity for a certain class of endomorphisms of ( ) with , ≥ 2; this kind of endomorphisms is obtained from vectorial difference equations where the mapping defining these equations satisfies a circulant matrix condition. The Strang-type preconditioner was also used to solve linear systems from differential-algebraic equations and delay differential equations; see [5][6][7][8].…”

Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

“…The reason why we focus our attention on skew-circulant operator is to explore the application of skew-circulant in the related field. On the basis of existing application situation [2][3][4][5][6][7][8], we will exploit solving ordinary, partial, and delay differential equations based on skew circulant operator.…”

“…Bertaccini and Ng [1] proposed a nonsingular skew-circulant preconditioner for systems of LMF-based ODE codes. Delgado et al [2] developed some techniques to obtain global hyperbolicity for a certain class of endomorphisms of ( ) with , ≥ 2; this kind of endomorphisms is obtained from vectorial difference equations where the mapping defining these equations satisfies a circulant matrix condition. Wilde [3] developed a theory for the solution of ordinary and partial differential equations whose structure involves the algebra of circulants.…”

Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers

“…By using a Strang-type block circulant preconditioner, Zhang et al [9] speeded up the convergent rate of boundary-value methods. Delgado et al [10] developed some techniques to obtain global hyperbolicity for a certain class of endomorphisms of ( ) with , ≥ 2; this kind of endomorphisms was obtained from vectorial difference equations where the mapping defining these equations satisfies a circulant matrix condition. In [11], nonsymmetric, large, and sparse linear systems were solved by using the generalized minimal residual (GMRES) method; a circulant block preconditioner was proposed to speed up the convergence rate of the GMRES method.…”