It is known that the critical condition which guarantees quadratic convergence of approximate Newton methods is an approximation of the identity condition. This requires that the composition of the numerical inversion of the Fréchet derivative with the derivative itself approximate the identity to an acc...
It is shown that the matrix sequence generated by Euler's method starting from the identity matrix converges to the principal pth root of a square matrix, ... Y Ling,Z Huang - 《Numerical Linear Algebra with Applications》 被引量: 3发表: 2017年 A "Square-root" Method for the Density Ma...
The use of exponential functions to fit decomposition datasets is common in scientific literature. Olson's exponential equation ( X t = X 0 e -kt) is widel... P Rovira,R Rovira - 《Geoderma》 被引量: 109发表: 2010年 Identity of simultaneous estimates of control points and of their esti...
Systems of Newton equations of the formq=12A1(q)kwith an integral of motion quadratic in velocities are studied. These equations generalize the potential case (whenA=I,the identity matrix) and they admit a curious quasi-Lagrangian formulation which differs from the standard Lagrange equations by...
In section 3, we prove the global convergence of the proposed algorithm. Some numerical tests are shown in Section 4 and a conclusion is given in section 5. Throughout this paper, we use ‖⋅‖ to denote the 2−norm and E denotes the identity matrix. 2. Algorithm We now describe ...
X is the saturated thickness divided by the cell thickness, Y is the value of the smoothing function, and Ω is the interval of X where the quadratic equation is applied, and is equal to 0.1 in this example (NWT input file variable THICKFACT). Description of MODFLOW-NWT 5 ...
Unfortunately, there is no magic formula that works well in all cases. We can use specic information about the problem, for instance by setting it to the inverse of an approximate Hessian calculated by nite differences at x0 . Otherwise, we can simply set it to be the identity matrix, ...
In doing so, we derive and discuss a discrete adaptive solution scheme, thereby trying to mimic the underlying continuous problem numerically without losing the famous quadratic convergence regime of the classical Newton method in a vicinity of a regular solution. The derivation of the proposed ...
where I n denotes the identity matrix of n × n . Then, any matrix A ( x ) that fulfills the following condition lim x → ξ A ( x ) = f ( 1 ) ( ξ ) − 1 guarantees that δ > 0 exists, such that iteration function Φ given by (11), fulfills a necessary (but no...
where I n denotes the identity matrix of n × n . Then, any matrix A ( x ) that fulfills the following condition lim x → ξ A ( x ) = f ( 1 ) ( ξ ) − 1 guarantees that δ > 0 exists, such that iteration function Φ given by (11), fulfills a necessary (but no...