Necessary and sufficient conditions for hypoelliptic of certain left invariant operators on nilpotent Lie groups II.
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 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.
Newton methods for solving two classes of nonsmooth equations
The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not...
Newton-Kantorovich method and its global convergence.
Newton's Method for Gradient Equations Based upon the Fixed Point Map: Convergence and Complexity Study.
Nonlinear iterative methods and parallel computation
Nonlinear reduction for solving deficient polynomial systems by continuation methods.
Nonlinear Successive Over-Relaxation.
Nonsmooth equations approach to a constrained minimax problem
An equivalent model of nonsmooth equations for a constrained minimax problem is derived by using a KKT optimality condition. The Newton method is applied to solving this system of nonsmooth equations. To perform the Newton method, the computation of an element of the -differential for the corresponding function is developed.
Non-uniqueness of almost unidirectional inviscid compressible flow
Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with...
Nullstelleneinschließung mit dem Newton-Verfahren ohne Invertierung von Intervallmatrizen.
Numerical bifurcation of separable parameterized equations.
Numerical computation of a nonlocal double obstacle problem.
Numerical Computation of Branch Points in Nonlinear Equations.
Numerical evidence for a conjecture in real algebraic geometry.
Numerical Solutions for some Coupled Systems of Nonlinear Boundary Value Problems.
Numerical Stability for Solving Nonlinear Equations.