1,721,012 research outputs found
Condizioni Necessarie per Problemi di Ottimizzazione in Presenza di Vincoli
No full textnota indirizzata agli studenti del corso di dottorato, sui moltiplicatori di Lagrange generalizzati e loro applicazioni alla programmazione matematica e al calcolo delle variazion
On functional iteration methods for solving nonlinear matrix equations arising in queueing problems
No full text
Solving certain queueing problems by means of regular splittings
No full textAbstractWe analyze the problem of the computation of the solution of the nonlinear matrix equation X = Σi=0+∞ XiAi, arising in queueing models. We propose a technique based on regular splittings, that on one hand leads to a new method for computing the solution, and on the other hand, it may be used to construct nonlinear matrix equations equivalent to starting one, that can be possibly solved by applying different algorithms
Separable Asymptotic Cost of Evaluating Elementary Functions
No full textThe computational cost, in the bit model of computation, of the evaluation of a real function f(x) in a point x is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on x also when x approaches a critical point for the function f. We investigate yhe hypotheses under which it is possible to give upper bounds on the cost as functions of "separated variables" d and x, that is as products of the two functions, each of one variable. We examine in particular the case of elementary functions
Non Recursive Solution of Sparse Block Hessenberg Systems
No full textA double-phase algorithm, based on the block recursive LU decomposition, has been recently proposed to solve block Hessenberg systems with sparsity properties. In the first phase the information
related to the factorization of A and required to solve the system, is computed and stored. The solution of the system is then computed in the second phase. In the present paper the algorithm is
modified: the two phases are merged into a one-phase version having the same computational cost and
allowing a saving of storage. Moreover, the corresponding non recursive version of the new algorithm is presented, which is especially suitable to solve infinite systems where the coefficient matrix dimension is not a-priori fixed and a subsequent size enlargement technique is
used. A special version of the algorithm, well suited to deal with block Hessenberg matrices having also a block band structure, is presented. Theoretical asymptotic bounds on the computational costs
are proved. They indicate that, under suitable sparsity conditions, the proposed algorithms outperform Gaussian elimination. Numerical experiments have been carried out, showing the
effectiveness of the algorithms when the size of the system is of practical interest
A Polynomial Fit Preconditioner for Band Toeplitz Matrices in Image Reconstruction
No full textThe preconditioned conjugate gradient (CG) is often applied in image reconstruction as a
regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We
introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit which has the same effectiveness of the previous ones but has a lower cost when applied to band matrices. The case of band block Toeplitz matrices with band Toeplitz blocks (BTTB) corresponding to separable point spread functions is also considered
A Family of Modified Regularizing Circulant Preconditioners for Two-levels Toeplitz Systems
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