Abstract
In this paper, two new analogues of the Hilbert matrix with four-parameters have been introduced. Explicit formulæ are derived for the LU-decompositions and their inverses, and the inverse matrices of these analogue matrices.
(Communicated by Milan Paštéka)
References
[1] Chu, W.—Di Claudio, L. V.: Binomial determinant evaluations, Ann. Comb. 9(4) (2005), 363–377.10.1007/s00026-005-0264-4Search in Google Scholar
[2] Chu, W.: Finite differences and determinant identities, Linear Algebra Appl. 430(1) (2009), 215–228.10.1016/j.laa.2007.08.044Search in Google Scholar
[3] KIlIç, E.—Prodinger, H.: A generalized Filbert matrix, Fibonacci Quart. 48(1) (2010), 29–33.Search in Google Scholar
[4] KIlIç, E.—Prodinger, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89(10) (2012), 1370–1377.10.1080/00207160.2012.687724Search in Google Scholar
[5] KIlIç, E.—Prodinger, H.: Variants of the Filbert matrix, Fibonacci Quart. 51(2) (2013), 153–162.Search in Google Scholar
[6] KIlIç, E.—Prodinger, H.: The generalized q-Pilbert matrix, Math. Slovaca 64(5) (2014), 1083–1092.10.2478/s12175-014-0260-4Search in Google Scholar
[7] KIlIç, E.—Prodinger, H.: Asymmetric generalizations of the Filbert matrix and variants, Publ. lnst. Math. (Beograd) (N.S.) 95(109) (2014), 267–280.10.2298/PIM1409267KSearch in Google Scholar
[8] KIlIç, E.—Prodinger, H.: The generalized Lilbert matrix, Period. Math. Hungar. 73(1) (2016), 62–72.10.1007/s10998-016-0128-1Search in Google Scholar
[9] KIlIç, E.—ArIkan, T.: A nonlinear generalization of the Filbert matrix and its Lucas analogue, Linear Multilinear Algebra 67(1) (2019), 141–157.10.1080/03081087.2017.1412393Search in Google Scholar
[10] KIlIç, E.—Koparal, S.—Ömür, N.: New asymmetric generalizations of the Filbert and Lilbert matrices, Period. Math. Hungar. 78 (2019), 231–241.10.1007/s10998-018-0253-0Search in Google Scholar
[11] KIlIç, E.—Koparal, S.—Ömür, N.: New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries, Hacet. J. Math. Stat., accepted, https://doi.org/10.15672/hujms.47349510.15672/hujms.473495Search in Google Scholar
[12] KIlIç, E.: The generalized Fibonomial matrix, European J. Combin. 31 (2010), 193–209.10.1016/j.ejc.2009.03.041Search in Google Scholar
[13] Merca, M.: A note on the determinant of a Toeplitz-Hessenberg matrix, Spec. Matrices 1 (2013), 10–16.10.2478/spma-2013-0003Search in Google Scholar
[14] Prodinger, H.: A generalization of a Filbert matrix with 3 additional parameters, Trans. R. Soc. S. Afr. 65(3) (2010), 169–172.10.1080/0035919X.2010.510718Search in Google Scholar
[15] Richardson, T.: The Filbert matrix, Fibonacci Quart. 39(3) (2001), 268–275.Search in Google Scholar
[16] Yang, S. L.—Dong, Y. N.: Hankel determinants of generalized factorials, Indian J. Pure Appl. Math. 49(2) (2018), 217–225.10.1007/s13226-018-0264-9Search in Google Scholar
[17] Zhou, J.—Jiang, Z.: The spectral norms of g-circulant matrices with classical Fibonacci and Lucas numbers entries, Appl. Math. Comput. 233 (2014), 582–587.10.1016/j.amc.2014.02.020Search in Google Scholar
[18] Zhou, J.—Jiang, Z.: Spectral norms of circulant-type matrices with Binomial coefficients and Harmonic numbers, Int. J. Comput. Methods 11(05) (2014), Art. ID 1350076.10.1142/S021987621350076XSearch in Google Scholar
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Articles in the same Issue
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs