Microlocal analysis for spatially inhomogeneous pseudo differential operators
Microlocal properties of a class of pseudodifferential operators with double involutive characteristics
Microlocalisation hypo-analytique et extension holomorphe de fonctions C. R.
Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité
Modifications of the continuation method for the solution of systems of nonlinear equations.
Monotone Iterative Methods for Finite Difference System of Reaction-Diffusion Equations.
Monotone Iterative Methods for Nonlinear Equations Involving a Noninvertible Linear Part.
Monotonically Convergent Iterative Methods for Nonlinear Systems of Equations.
Monotonieeigenschaften des Steffensen-Verfahrens.
Multiparameter extrapolation and deflation methods for solving equation systems.
Multiple root finder algorithm for Legendre and Chebyshev polynomials via Newton's method.
Multivariate secant method
Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.
The main purpose of this note is to show how Sturm-Habicht Sequence can be generalized to the multivariate case and used to compute the number of real solutions of a polynomial system of equations with a finite number of complex solutions. Using the same techniques, some formulae counting the number of real solutions of such polynomial systems of equations inside n-dimensional rectangles or triangles in the plane are presented.
Necessary and sufficient conditions for hypoelliptic of certain left invariant operators on nilpotent Lie groups II.
New algorithm for polynomial spectral factorization with quadratic convergence. II
New algorithm for polynomial spectral factorization with quadratic convergence. I
New Einstein metrics on which are non-naturally reductive
We prove that there are at least two new non-naturally reductive invariant Einstein metrics on . It implies that every compact simple Lie group ...
New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations
In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682. We describe the analysis of the proposed methods along with numerical experiments including comparison...
New quasi-Newton method for solving systems of nonlinear equations
We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires arithmetic operations per iteration in contrast with the Newton method, which requires operations per iteration. Computational experiments confirm the high efficiency...
New sufficient convergence conditions for the secant method
We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses “Lipschitz-type” and center-“Lipschitz-type” instead of just “Lipschitz-type” conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.