We introduce fractal Newton methods for solving f(x)=0 that generalize and improve the classical method. compare theoretical efficacy of illustrate theory with examples.

In April 2001 SN1993J was observed with both the PN and MOS cameras of the XMM-Newton observatory, resulting in about 7 × 10 4 s of acceptable observation time. Fit results with both the PN and MOS2 camera spectra studying different spectral models are presented. The spectra are best fitted in the energy range between 0.3 and ∼ 10 keV by a 2-component thermal model with temperatures of kT1 = 0....

In [Cha00] Chai made a conjecture on the codimensions of Newton strata in Shimura varieties, which then led Rapoport [Rap05] to his conjecture on dimensions of affine Deligne-Lusztig varieties inside affine Grassmannians. The main goal of this paper is to show that exactly the same codimensions arise in a simpler context, that of the Newton stratification in the adjoint quotient of a reductive ...

We have conducted a survey of X-ray sources in XMM-Newton observations of M31, examining their power density spectra (PDS) and spectral energy distributions (SEDs). Our automated source detection yielded 535 good X-ray sources; to date, we have studied 225 of them. In particular, we examined the PDS because low mass X-ray binaries (LMXBs) exhibit two distinctive types of PDS. At low accretion r...

The spectra of several X–ray binary pulsars display a clear soft excess, which in most cases can be described with a blackbody model, above the main power–law component. While in the high–luminosity sources it is usually characterized by low temperature (kT < 0.5 keV) and large emission radius (R > 100 km), in the two persistent and low–luminosity pulsars 4U 0352+309 and RX J0146.9+6121 this co...

A novel computational approach is introduced for the efficient computation of equilibrium solutions of seasonally forced ocean biogeochemical models. The essential idea is to formulate the problem as a large system of nonlinear algebraic equations to be solved with a class of methods known as matrix-free Newton–Krylov (MFNK). MFNK is a combination of Newton-type methods for superlinearly conver...

We analyze the XMM-Newton dataset of the interacting cluster of galaxies Abell 3528 located westward in the core of the Shapley Supercluster, the largest concentration of mass in the nearby Universe. A3528 is formed by two interacting clumps (A3528-N at North and A3528-S at South) separated by 0.9 h −1 70 Mpc at redshift 0.053. XMM-Newton data describe these clumps as relaxed structure with an ...

In this paper, we investigate the convergence behaviour of a class of regularized Newton methods for the solution of nonlinear inverse problems. In order to keep the overall numerical effort as small as possible, we propose to solve the linearized equations by certain semiiterative regularization methods, in particular, iterations with optimal speed of convergence. Our convergence rate analysis...