Calcolo
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Multigrid methods for toeplitz matrices
Calcolo - Tập 28 - Trang 283-305 - 1991
We introduce a class of Multigrid methods for solving banded, symmetric Toeplitz systems Ax=b. We use a, special choice of the projection operator whose coefficients simply depend on some spectral properties of A. This choice leads to an iterative Multigrid method with convergence rate smaller than 1 independent of the condition number K2(A) and of the dimension of the matrix. In the second part t......
On the number of transitive digraphs withn labeled vertices andk arcs
Calcolo - Tập 17 - Trang 365-378 - 1980
A computer determination of the numberT
n,k of transitive digraphs onn labeled vertices andk arcs is obtained for 2≤n≤6,0 ≤k≤n
2-n. Furthermore some formulae are given for determiningT
n,k, ∇n for extremal values ofk (namely, 0≤k≤6 andn
2
-3n+4≤k≤n
2-n).
Accelerazione della convergenza per metodi di risoluzione di equazioni differenziali ordinarie
Calcolo - Tập 11 - Trang 509-520 - 1974
In questo lavoro si è elaborato un procedimento di accelerazione della convergenza che permette di raddoppiare l'ordine dei metodi multistep, per la risoluzione numerica dell'equazione differenziale ordinaria
$$y' = f(x,y),y_0 = y(x_0 );{}_{x_0 }^x \in [a,b].$$
Tale accelerazione è appl......
Linear programming selection of internal financial laws and a knapsack problem
Calcolo - Tập 37 - Trang 47-57 - 2000
We formulate and solve explicitly a linear programming problem that arises from the problem of choosing an internal financial law of a given financial project such that the associated discount vector maximizes a linear objective function. If the original problem has optimal solutions, then it is equivalent to a knapsack problem. We obtain its basic optimal solutions in closed form. After consider......
Scattered data interpolation of Radon data
Calcolo - Tập 48 - Trang 5-19 - 2010
Linear combinations of translates of a given basis function have long been successfully used to solve scattered data interpolation and approximation problems. We demonstrate how the classical basis function approach can be transferred to the projective space ℙd−1. To be precise, we use concepts from harmonic analysis to identify positive definite and strictly positive definite zonal functions on ℙ......
Systematic construction of optimal linear recurrent codes for burst error correction
Calcolo - Tập 1 - Trang 147-153 - 1964
A method is presented for the construction of binary linear burst error correcting recurrent codes of type B2, viz. those codes which correct any burst of lengthl=rb or less provided it is confined amongr successive blocks of lengthb. The proposed codes are optimal in the sense they meet the lower bound obtained by Wyner and Ash, and are constructed through a particular bordering of the characteri......
Computations concerning Waring's problem for cubes
Calcolo - Tập 19 - Trang 415-431 - 1982
Waring's problem for cubes is investigated using numerical computations. The densities of number not representable as a sum of four and five cubes are computed in large intervals. Extrapolation of these data allows us to conjecture on the order of magnitude of last exceptions. The representability with four relative cubes and the validity of the theoretical asymptotic formula are investigated too.......
Convergence and comparison results for double splittings of Hermitian positive definite matrices
Calcolo - Tập 44 - Trang 127-135 - 2007
For single splittings of Hermitian positive definite matrices, there are well-known convergence and comparison theorems. This paper gives new convergence and comparison results for double splittings of Hermitian positive definite matrices. Keywords: Hermitian positive definite matrix; convergence theorem; comparison theorem; double splitting Mathematics Subject Classification (2000): 65F10
On the degeneracy property of some linear positive operators
Calcolo - Tập 25 - Trang 363-377 - 1988
The degeneracy property of a wide class of linear positive operators is investigated; a short proof of a Passow's conjecture is given for this class. Finally an application of these results in CAGD is also discussed.
Numerical methods for a class of nonlinear integro-differential equations
Calcolo - Tập 50 - Trang 17-33 - 2012
In a previous article (Glowinski, J. Math. Anal. Appl. 41, 67–96, 1973) the first author discussed several methods for the numerical solution of nonlinear equations of the integro-differential type with periodic boundary conditions. In this article we discuss an alternative methodology largely based on the Strang’s symmetrized operator-splitting scheme. Several numerical experiments suggest that t......
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