In this paper the iterative methods, namely NEWTON, quasi-NEWTON and Broyden are studied. Convergence rate and accuracy of these three methods are investigated and the results are presented in tables and diagrams. Also, NEWTON and quasi-NEWTON methods are studied for unconstraint optimization method with the second order derivative. We will present an algorithm to minimize the calculation without losing advantages of stability. We see that it is not needed to compute Q for each iterative in decomposition process.

Some of important issues in acoustic echo cancellation (AEC) using adaptive filters are the sparseness of the acoustic path impulse responses and strong dependency of the convergence performance of adaptive algorithm to the eigenvalue spread of the input signal correlation matrix. These issues result in a performance degradation of the adaptive AEC systems. In this paper, to improve the performance of the LMS/NEWTON adaptive algorithm in AEC, the matrix inverse computation is modified. To this end, the matrix inversion lemma is employed such that the contribution of the matrix inverse in the weight update is initially high and as a result, the dependency of the adaptive algorithm to the eigenvalue spread is low during the initial convergence. In addition, for the step-size adjustment, an improved proportionate method is applied such that during the convergence, the contribution of those weights having higher amplitudes in the adaptation process is gradually varied to become identical at the end of convergence. The proposed adaptive proportionate method, results in both convergence rate and steady-state performance improvement for identification of sparse acoustic impulse responses. Simulation results using a colored speech-like signal shows the steady-state misalignment of the proposed algorithm is typically 6. 5 dB lower than that of the LMS/NEWTON algorithm. Moreover, the convergence of the proposed algorithm is typically 3. 6 sec faster than that of the PNLMS algorithm, to achieve a misalignment of-17 dB. Theoretical misalignment analyses in the transient and steady state are presented and verified with simulation results.

In this paper, a class of new polynomials based on Fibonacci sequence using NEWTON INTERPOLATION is introduced. This target is performed once using NEWTON forward-divided-difference formula and another more using NEWTON backward-divided-difference formula. Some interesting results are obtained for forward and backward differences. The relationship between forward (and backward) differences and the Khayyam-Pascal’, s triangle are also examined.

Today, the significance of the velocity model estimation in seismic migration as well as time to depth conversion of seismic sections is very clear to every geophysicist. From a practical point of view, approaches such as well logging techniques or direct observations cannot provide a reliable description of regional scale physical properties of the earth. Seismic imaging is a tool to describe the earth physical properties. Today, one of the imaging techniques, which is highly welcomed by geoscientists is the full waveform inversion (FWI). The full waveform inversion-an efficient method in seismic imaging-uses all available information in the seismograms, including the amplitude, phase, and the first arrival time so as to judge the physical properties of the earth. In fact, FWI is represented as an optimization problem by defining a misfit function, which measures differences between the observed waveforms and the computed waveforms. In FWI, the size of the model space parameters will not allow us using global minimization algorithms. Therefore, we minimize the misfit function by local optimization methods. A waveform inversion problem is usually solved repetitively by the gradient-based solutions. In this paper, we have compared two gradient optimization algorithms of Gauss-NEWTON algorithm based on the main diagonal of the pseudo Hessian matrix (GN-DPH) and the limited memory-BFGS (LBFGS). Although the L-BFGS does not need the computation of Hessian matrix, but according to the numerical tests on synthetic models, we have found that GN-DPH algorithm results are more accurate than L-BFGS after 40 iterations.....

The conflict between the NEWTONian and the Leibnizian picture of spacetime is well-known and widely discussed in the literature. However, two competing metaphysical pictures of spacetime have not been addressed so far: The NEWTONian and the Lagrangian pictures. According to the NEWTONian picture, spacetime can be considered as the time evolution of a spatial hypersurface. According to the Lagrangian picture, spacetime is a unified whole that can be examined in an all-at-once manner, and its (temporal) evolution is not meaningful, except locally or quasi-locally. Although the NEWTONian picture has been the dominant metaphysical picture since NEWTON's time, our explicit familiarity with these two competing pictures is recent. It is rooted in Smolin's criticism of modern cosmology and Wharton's research on the foundations of quantum mechanics. Here, we describe the views of Smolin and Wharton, then we will argue that two famous formulations of general relativity, namely the Hamiltonian formulation and the Lagrangian formulation, require the NEWTONian and the Lagrangian picture, respectively. Also, we will argue that: (1) the Lagrangian picture is more compatible with the philosophy of relativity theory than the NEWTONian picture, while the NEWTONian picture is only acceptable for practical and computational purposes. And, (2) the Lagrangian picture is universal and applicable to any spacetime, while the NEWTONian picture can only be used for certain spacetimes. Therefore, the Lagrangian picture is a more plausible metaphysical picture than the NEWTONian.

NEWTON’ s world consists of atoms, which cause natural phenomena with their movement through vacuum. Force is another important element of NEWTON’ s world. NEWTON denies the idea that gravity is an essential property of matter. This indicates his adherence to the traditional conception of substance. Moreover, it provides a reason for him to believe in divine omnipresence. Other components of NEWTON’ s ontology are space and time. He believes in absolute space and time and that it is God who sustains space and time, with his omnipresence. Every being, including God, exists in space and time. And since absolute space and time are God’ s frame of action, contemplating about nature is a way to know God. NEWTON believes that his philosophy rejects material philosophy and proves an intelligent Creator and his continual action in the world. The aim of this article is to present a comprehensive image of NEWTON’ s ontology, based on an investigation into his ideas about the material world, space, time and God.

Introduction: To estimate the accuracy levels of Lagrange, NEWTON backward INTERPOLATION, and linear INTERPOLATION methods in estimating the output factors for square fields used in linear accelerator for 6 MV photons at various depths. Materials and Methods: Ionization measurements were carried out in radiation field analyzer in linear accelerator for 6 MV beams at the depths of 5 and 10 cm by 0. 6 cc Farmer-type ionisation chamber. Dosimetry was performed by ion collection method with 0. 5 cm2 interval for square fields from 4 × 4 cm2 to 40 × 40 cm2 field sizes. The measured output factor values for 10 square field sizes with equal interval were taken for interpolating the intermediate square field size values. The Lagrange and NEWTON backward methods were used for predicting the intermediate output factors. Results: The percentage of deviation from the measured value was estimated for all the three methods. The calculated output factor values of the two proposed methods were compared with the standard linear INTERPOLATION method used in routine clinical practice. It was observed that the Lagrange and NEWTON backward methods were not significantly different from the measured value (P=0. 77). The linear INTERPOLATION values were significantly different from the measured value (P<0. 01). Conclusion: It is recommended to use the Lagrange and NEWTON backward INTERPOLATION methods to estimate the intermediate output factors to increase accuracy in treatment delivery. The routine linear INTERPOLATION method can be applied only for small intervals. This proposed INTERPOLATION method is highly associated with the measured values in all the interval levels.