P. L. Chebyshev, "Sur l'interpolation par la methode des moindres carres", Mem. Acad. Imper. Sci. St. Petersbourg (7) 1 (15), 1859, 1 -- 24, also: Oeuvres I, 473 -- 489. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Generalized Schur Algorithm for the Superfast Solution of.. - Ammar, Gragg (1987) (13 citations) (Correct)
....matrices, Szego polynomials and Schur s algorithm [25] In particular, the deHoog Musicus algorithm is naturally explained in terms of a generalization of Schur s algorithm. An analogous treatment of the positive definite Hankel case, M = j k ] M # 0, generalizing the algorithm of Chebyshev [7, 12], is given in [18] In Section 2 we review the classical foundations of fast Toeplitz solvers. We present the generalized Schur algorithm in Section 3 and describe the use of the algorithm for the superfast solution of a positive definite Toeplitz system in Section 4. Before proceeding, we note ....
....formula. We now describe an algorithm for finding the Cholesky factors L n and D n of M n (also see [22] We will see that this algorithm is a manifestation of the classical algorithm of Schur. The algorithm presented below is in direct analogy with the derivation of Chebyshev s algorithm [7] for positive definite Hankel matrices, as presented, for instance, by Gautschi [12] Extend the functional to certain pairs of Laurent polynomials by putting : j k , j k n. Then # j,k : # , # k 8 # j,k : # # k are defined for 0 n and n k j ....
P. L. Chebyshev, Sur l'Interpolation par la Methode des Moindres Carres, Mem. Acad. Imper. Sci. St. Petersbourg, 1 (1859), 1-24.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
....function is 1 4x # 1 8x 12x 2 2x 2 . Lower triangular matrices L n as defined by (5.1) are also closely related to the Lanczos algorithm. Observe that with (5. 3) we obtain the parameters in the three term recursion in a form which was already known to Chebyshev in his algorithm in [19], p. 482, namely # 1 = l(1, 0) l(0, 0) and # j 1 = l(j 1,j) l(j, j) l(j, j 1) l(j 1,j 1) # j = l(j, j) l(j 1,j 1) for j # 1. 5.5) the electronic journal of combinatorics 8 2001, #A1 21 Since further l(m, 0) c m for all m # 0 by (5.3) it is l(m 1, 1) l(m, ....
P. L. Chebyshev, "Sur l'interpolation par la methode des moindres carres", Mem. Acad. Imper. Sci. St. Petersbourg (7) 1 (15), 1859, 1 -- 24, also: Oeuvres I, 473 -- 489.
On some Structured Inverse Eigenvalue Problems - Erra, Philippe (1995) (2 citations) (Correct)
....for solving a (Jiep) We have seen that constructing a Jacobi matrix is equivalent to construct a sequence of orthogonal polynomials. We must point out that the two oldest known procedures for generating orthogonal polynomials, are the Stieltjes procedure ( Sti84] and the Chebyschev procedure ([Che58, Che59]) Both algorithms compute a sequence of orthogonal polynomials with a forward process, i.e they compute p k before p k 1 . The Stieltjes procedure has been studied by Gautschi [Gau82, Gau85] and the Chebyshev procedure has been also advocated by Gautschi [Gau82] and by Gutknecht and Gragg ....
P. Chebyshev. Sur l'interpolation par la m'ethode des moindres carr'es. M'em. Acad. Imp. des Sci. St. Petersbourg, s'erie 7, 1:1--24, 1859.
Chebyshev's Recursion - Some Analytical, Computational .. - Korzh, Ovcarenko.. Self-citation (Chebyshev) (Correct)
....suggestive of some unknown potential that the methods of the moment problem may possess, and may serve to clarify its essence. In 1859 P.L. Chebyshev proposed an effective technique to construct the system of polynomials orthogonal with respect to some measure on the real line by its power moments [2]. The Chebyshev algorithm actually realizes a transition from one system of polynomials with three term recurrence relations to the other system of polynomials orthogonal with respect to some given measure on IR 1 . It turned out that the Chebyshev idea is applicable to different problems. ....
....recurrence relation Pn 1 ( Gamma an )Pn ( Gamma b n Pn Gamma1 ( P Gamma1 ( j 0; P 0 ( j 1; where the constants a k ; b k are known. The sets of coefficients fa k ; b k g and fba k ; b b k g are connected with each other by a remarkable relation that goes back to P.L. Chebyshev [2]. The algorithm presented below is a direct generalization of the original Chebyshev algorithm. In stating the modified Chebyshev algorithm we will in principal follow [6] Definition. The matrix T b P;P of the modified moments, where kT b P;P k k;l = oe k;l def = b P k ; P l ; 2:15) ....
Chebyshev, P.L. (1859): Sur l'interpolation par la m'ethode des moindres carr'es, M'em.Acad.Imper.Sci. St.Petersbourg. 7, 1, 15, 1--24
Hankel Matrices in Coding Theory and Combinatorics - Tamm (2000) (Correct)
No context found.
P. L. Chebyshev, "Sur l'interpolation par la methode des moindres carres", Mem. Acad. Imper. Sci. St. Petersbourg (7) 1 (15), 1859, 1 -- 24, also: Oeuvres I, 473 -- 489.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
No context found.
P. L. Chebyshev, "Sur l'interpolation par la methode des moindres carres", Mem. Acad. Imper. Sci. St. Petersbourg (7) 1 (15), 1859, 1 -- 24, also: Oeuvres I, 473 -- 489.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC