Geodesic
Nonnegative Solutions to Systems with Symmetric Circulant Matrix
Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 170-180.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a system with symmetric circulant matrix, conditions on the right-hand side vector which ensure the positivity of the solution to the system are found. As an application of the results obtained, the problem of positive spline interpolation of positive functions on uniform grids is studied. 
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Yu. S. Volkov. Nonnegative Solutions to Systems with Symmetric Circulant Matrix. Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 170-180. http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a1/

[1] Miroshnichenko V. L., “Convex and monotone spline interpolation”, Constructive Theory of Functions'84, Proceed. Intern. Conf. (Varna), Publ. House of Bulgarian Acad. of Sci., Sofia, 1984, 610–620

[2] Verlan I. I., Konservativnaya interpolyatsiya obobschennymi splainami, Avtoreferat diss. ... k. f.-m. n., MGU, M., 1989

[3] Zavyalov Yu. S., “Monotonnaya interpolyatsiya obobschennymi kubicheskimi splainami klassa $C^2$”, Interpolyatsiya i approksimatsiya splainami, Vychislitelnye sistemy. Vyp. 147, IM SO RAN, Novosibirsk, 1992, 44–67 | MR

[4] Zavyalov Yu. S., “Vypuklaya interpolyatsiya obobschennymi kubicheskimi splainami klassa $C^2$”, Splainy i ikh prilozheniya, Vychislitelnye sistemy. Vyp. 154, IM SO RAN, Novosibirsk, 1995, 15–64

[5] Zavyalov Yu. S., “O neotritsatelnom reshenii sistemy uravnenii s nestrogo yakobievoi matritsei”, Sib. matem. zh., 37:6 (1996), 1303–1307 | MR | Zbl

[6] Markus M., Mink Kh., Obzor po teorii matrits i matrichnykh neravenstv, Nauka, M., 1972

[7] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972 | Zbl

[8] Kindalev B. S., “Tochnaya otsenka normy obratnoi matritsy dlya simmetricheskogo tsirkulyanta”, Approksimatsiya splainami, Vychislitelnye sistemy. Vyp. 121, IM SO AN SSSR, Novosibirsk, 1987, 37–45 | MR

[9] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | Zbl

[10] Albasiny E. L., Hoskins W. D., “Explicit error bounds for periodic splines of odd order on a uniform mesh”, J. Inst. Math. Appl., 12:3 (1973), 303–318 | DOI | MR | Zbl

[11] Spravochnik po spetsialnym funktsiyam, eds. Abramovits M., Stigan I., Nauka, M., 1979

[12] Kindalev B. S., “Asimptotika pogreshnosti i superskhodimost periodicheskikh interpolyatsionnykh splainov chetnoi stepeni”, Splainy v vychislitelnoi matematike, Vychislitelnye sistemy. Vyp. 115, IM SO AN SSSR, Novosibirsk, 1986, 3–25 | MR