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Remarks on inverse of matrix polynomials

Fischer, Cyril, Náprstek, Jiří (2017)

Programs and Algorithms of Numerical Mathematics

Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...

Résolubilité Gevrey d'opérateurs différentiels à coefficients constants

Giuseppe Zampieri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si discute l'esistenza di soluzioni Γ ( d ) su insiemi aperti Ω ⊂ ℝ n per equazioni differenziali iperbolico-ipoellittiche. Si dà una caratterizzazione geometrica quasi completa per aperti Ω ⊂ ℝ 2 .

Semi-smooth Newton methods for the Signorini problem

Kazufumi Ito, Karl Kunisch (2008)

Applications of Mathematics

Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.

Some convergence acceleration processes for a class of vector sequences

G. Sedogbo (1997)

Applicationes Mathematicae

Let ( S n ) be some vector sequence, converging to S, satisfying S n - S ∼ ϱ n n θ ( β 0 + β 1 n - 1 + β 2 n - 2 + . . . ) , 0 | ϱ | 1 , θ 0 , where β 0 ( ≠ 0 ) , β 1 , . . . are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.

Some notes on the quasi-Newton methods

Masanori Ozawa, Hiroshi Yanai (1982)

Aplikace matematiky

A survey note whose aim is to establish the heuristics and natural relations in a class of Quasi-Newton methods in optimization problems. It is shown that a particular algorithm of the class is specified by characcterizing some parameters (scalars and matrices) in a general solution of a matrix equation.

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