new homotopic factorization and symmetrization techniques for newton s and newton structured iteration we modify our earlier homotopic continuation process for iterative matrix inversion to improve the choice of the initial approximate inverse at every homotopic step this enables us to control the condition of the auxiliary matrices and to accelerate the convergence of the iteration the algorithm also extends our earlier approach where we factorized the input matrix into the product of better conditioned factors we accelerate our new algorithm in the case of a toeplitz like input comment on the extensions to the computations with other structured matrices such as cauchy pick and banded matrices and propose new techniques for the compression of the displacement of hermitian matrices

the method of particular solutions for solving nonlinear poisson problems abstract based on the recent development in the method of particular solutions we re exam three approaches using different basis functions for solving nonlinear poisson problems we further propose to simplify the solution procedure by removing the insolvency condition when the radial basis functions are augmented with high order polynomial basis functions we also specify the deficiency of some of these methods and provide necessary remedy the traditional picard method is introduced to compare with the recent proposed methods using matlab optimization toolbox solver for solving nonlinear poisson equations ranking on these three approaches are given based on the results of numerical experiment

a note on computational algorithm for the inverse of a square matrix this short note gives some comments on computational algorithm for inverse of a square matrix considered in paper h saberi najafi m shams solary computational algorithms for computing the inverse of a square matrix quasi inverse of a non square matrix and block matrices appl math comput in press doi 10 1016 j amc 2006 05 108 and supplements the discussion on this topic

determining surface temperatures from interior observations we consider the inverse heat transfer problem for the case of the one dimensional heat equation in a quarter plane and present a new solution algorithm together with error bounds of logarithmic convexity type our method is based on regularizing the initial value problem for the heat equation run sideways we describe a numerical experiment with rapidly varying temperature profiles and explain how the method can be extended to problems with temperature dependent thermal properties

block ilu factorization preconditioners for a block tridiagonal h matrix abstract we propose new parallelizable block ilu incomplete lu factorization preconditioners for a nonsymmetric block tridiagonal h matrix theoretical properties of these block ilu preconditioners are compared with those of block ilu preconditioners for the corresponding comparison matrix numerical results of the bicgstab using these block preconditioners are compared with those of the bicgstab using a standard ilu factorization preconditioner to see the effectiveness of the block ilu preconditioners lastly parallel computations of the block ilu preconditioners are carried out and evaluated on the cray c90

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

finding generalized inverses by a fast and efficient numerical method in this paper a method with very high order of convergence is constructed and analyzed the method is used to compute generalized inverses the efficiency index has been employed to show its superiority numerical experiments re verify that the proposed iterative expression is more effective than the existing methods of the same type

crossing of two mobile averages a method for measuring the roughness exponent self affine signals characterized by a defined hurst roughness exponent h can be investigated through mobile averages the density ensuremath rho of crossing points between any two moving averages is a measure of long range power law correlations in the signal the method is compared to the detrended fluctuation analysis we take advantage of our findings in order to propose a practically powerful and accurate technique for determining h and apply it right away to cases with persistent or antipersistent correlations

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

computational algorithms for computing the inverse of a square matrix quasi inverse of a non square matrix and block matrices in this paper we have written out some methods to find the inverse of a non singular matrix and also the quasi inverse of a singular matrix the corresponding algorithms have been used to solve the linear system of equations ax b as x a 1b a comparison table of the numerical results has been designed in each case to compare the implementation of the algorithms with each other the important part of the paper is presenting a block matrix method for finding the inverse matrix the block method finds the inverse matrix with a simple and easy algorithm

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

are crude oil markets multifractal evidence from mf dfa and mf ssa perspectives abstract in this article we investigated the multifractality and its underlying formation mechanisms in international crude oil markets namely brent and wti which are the most important oil pricing benchmarks globally we attempt to find the answers to the following questions 1 are those different markets multifractal 2 what are the dynamical causes for multifractality in those markets if any to answer these questions we applied both multifractal detrended fluctuation analysis mf dfa and multifractal singular spectrum analysis mf ssa based on the partition function two widely used multifractality detecting methods we found that both markets exhibit multifractal properties by means of these methods furthermore in order to identify the underlying formation mechanisms of multifractal features we destroyed the underlying nonlinear temporal correlation by shuffling the original time series thus we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non gaussian distribution at last by tracking the evolution of left and right half multifractal spectra we found that the dynamics of the large price fluctuations is significantly different from that of the small ones our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets but also the sources of multifractality and plausible explanations to current literature furthermore we investigated the different dynamical price behaviors influenced by large and small price fluctuations

fourier regularization method of a sideways heat equation for determining surface heat flux we consider a non standard inverse heat conduction problem in a quarter plane which appears in some applied subjects we want to know the surface heat flux in a body from a measured temperature history at a fixed location inside the body this is an exponentially ill posed problem in the sense that the solution if it exists does not depend continuously on the data a fourier regularization method together with order optimal logarithmic stability estimates is given a numerical example shows that the theoretical results are valid

nonlinear structure analysis of carbon and energy markets with mfdcca based on maximum overlap wavelet transform abstract this paper investigates the nonlinear structure between carbon and energy markets by employing the maximum overlap wavelet transform modwt as well as the multifractal detrended cross correlation analysis based on maximum overlap wavelet transform mfdcca modwt based on the modwt multiresolution analysis and the statistic q c c m significance relatively significant cross correlations are obtained between carbon and energy future markets either on different time scales or on the whole the result of the granger causality test indicates bidirectional granger causality between carbon and electricity future markets although the granger causality relationship between the carbon and oil price is not evident the existence of multifractality for the returns between carbon and energy markets is proven with the mfdcca modwt algorithm in addition results of investigating the origin of multifractality demonstrate that both long range correlations and fat tailed distributions play important roles in the contributions of multifractality

on the diagonal approximation of full matrices in this paper the construction of diagonal matrices in some sense approximating the inverse of a given square matrix is described the matrices are constructed using the well known computer algebra system maple the techniques we show are applicable to square matrices in general results are given for use in parallel diagonal implicit runge kutta pdirk methods for an s stage radau iia corrector we conjecture s possibilities for the diagonal matrices

on the scaling ranges of detrended fluctuation analysis for long term memory correlated short series of data abstract we examine the scaling regime for the detrended fluctuation analysis dfa the most popular method used to detect the presence of long term memory in data and the fractal structure of time series first the scaling range for dfa is studied for uncorrelated data as a function of time series length l and the correlation coefficient of the linear regression r 2 at various confidence levels next a similar analysis for artificial short series of data with long term memory is performed in both cases the scaling range is found to change linearly both with l and r 2 we show how this dependence can be generalized to a simple unified model describing the relation l r 2 h where h 1 2 h 1 stands for the hurst exponent of the long range autocorrelated signal our findings should be useful in all applications of dfa technique particularly for instantaneous local dfa where a huge number of short time series has to be analyzed at the same time without possibility of checking the scaling range in each of them separately

additive preconditioning and aggregation in matrix computations we combine our novel svd free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations our analysis and experiments show the power of our algorithms guide us in selecting most effective policies of preconditioning and aggregation and provide some new insights into these and related subjects compared to the popular svd based multiplicative preconditioners our additive preconditioners are generated more readily and for a much larger class of matrices furthermore they better preserve matrix structure and sparseness and have a wider range of applications e g they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem

comparative analysis of grey detrended fluctuation analysis methods based on empirical research on china s interest rate market abstract this study empirically compares the development of china s interest rate market in the past decade the yield of shibor market from 2006 to 2016 showed anti persistence and the later five year trend was stronger than that in the previous half period indicating a significantly growing trend of china s interest rate market we perform a comparative analysis of detrended fluctuation analysis dfa detrending moving average dma algorithm and the maximum overlap wavelet transform dfa modwt using grey and original sequences the autoregressive integrated moving average model is adopted to generate set point h sequences results illustrated that 1 for original sequences both the dfa modwt and dma 0 5 shows outstanding performances when the set hurst exponents are 0 6 and 0 7 and 0 8 and 0 9 respectively 2 for grey sequences g dfa performs best among the three methods followed by g dma and g dfa modwt 3 the long range correlation of the original sequences is slightly lower than the set values on the contrary the long range correlation of grey sequences is much higher than the set values thus the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence our results show that the grey sequence can determine the regular pattern from the messy sequence however grey sequences tend to be overly analyzed and misleading when large volumes of data are involved empirical studies confirm that china s interest rate market remains an inefficient market

a modified regularization method for a cauchy problem for heat equation on a two layer sphere domain in this paper we study a non characteristic cauchy problem for a radially symmetric inverse heat conduction equation in a two layer domain this is a severely ill posed problem in the sense that the solution if it exists does not depend continuously on the data it is well known that the classical tikhonov regularization solutions are too smooth and the approximate solutions may lack details that might be contained in the exact solutions combining fourier transform technique with a modified version of the classical tikhonov regularization we obtain a regularized solution which is stably convergent to the exact solution with a sharp error estimate

an iterative method for computing the approximate inverse of a square matrix and the moore penrose inverse of a non square matrix in this paper an iterative scheme is proposed to find the roots of a nonlinear equation it is shown that this iterative method has fourth order convergence in the neighborhood of the root based on this iterative scheme we propose the main contribution of this paper as a new high order computational algorithm for finding an approximate inverse of a square matrix the analytical discussions show that this algorithm has fourth order convergence as well next the iterative method will be extended by theoretical analysis to find the pseudo inverse also known as the moore penrose inverse of a singular or rectangular matrix numerical examples are also made on some practical problems to reveal the efficiency of the new algorithm for computing a robust approximate inverse of a real or complex matrix

approximate iterations for structured matrices important matrix valued functions f a are e g the inverse a 1 the square root sqrt a and the sign function their evaluation for large matrices arising from pdes is not an easy task and needs techniques exploiting appropriate structures of the matrices a and f a often f a possesses this structure only approximately however intermediate matrices arising during the evaluation may lose the structure of the initial matrix this would make the computations inefficient and even infeasible however the main result of this paper is that an iterative fixed point like process for the evaluation of f a can be transformed under certain general assumptions into another process which preserves the convergence rate and benefits from the underlying structure it is shown how this result applies to matrices in a tensor format with a bounded tensor rank and to the structure of the hierarchical matrix technique we demonstrate our results by verifying all requirements in the case of the iterative computation of a 1 and sqrt a

an efficient computation of generalized inverse of a matrix abstract we propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves 18th order of convergence by using only seven matrix multiplications per iteration loop this yields a high efficiency index for that computational task the algorithm has a relatively mild numerical instability and we stabilize it at the price of adding two extra matrix multiplications per iteration loop this implies an efficiency index that exceeds the known record for numerically stable iterations for this task which means substantial acceleration of the long standing algorithms for an important problem of numerical linear algebra our numerical tests cover a variety of examples in the category of generalized inverses such as drazin case rectangular case and preconditioning of linear systems the test results are in good accordance with our formal study

multifractality attributed to dual central limit like convergence effects abstract multifractals can be defined as fractal systems that express a range of fractal dimensions the origins of multifractality in time series data have conventionally been attributed to fat tailed probability distributions and to long range correlations multifractal sequences can be generated from the eigenvalue deviations of the gaussian unitary and orthogonal ensembles of random matrix theory these deviations can be resolved into component monofractal sequences governed by the tweedie compound poisson distribution a statistical model that expresses a variance to mean power law related to long range correlations fully multifractal descriptions of these deviations can be constructed provided that the parameter of the compound poisson model related to fractal dimension varies in accordance with an asymmetric laplace distribution both the tweedie compound poisson distribution and the asymmetric laplace distribution serve as foci of convergence in limit theorems on independent and identically distributed random variables the hypothesis that multifractal sequences can be attributed to mathematical convergence effects that have as their focus these two statistical models is proposed

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

an improvement on a new upper bound for moduli of eigenvalues of iterative matrices in this paper some improvements on int j comput math 80 june 2003 799 803 are presented for a bound for moduli of eigenvalues of iterative matrices and subsequently we investigate the relationships among them and show that the new bounds are better than the earlier ones int j comput math 53 1994 203 217 j comput math 7 2 1986 41 46 int j comput math 80 june 2003 799 803 under some conditions

an efficient maps for solving fourth order partial differential equations using trigonometric functions abstract in this paper we apply the method of approximate particular solutions maps based on the trigonometric functions to solve the fourth order partial differential equations pdes through the use of particular solutions of two second order differential equations the derivation of the closed form particular solutions for higher order pdes is a challenge and could be tedious such task can be achieved by a simple algebraic procedure to alleviate the difficulty of the derivation of particular solutions for fourth order pdes since the closed form particular solutions for the second order pdes with constant coefficients are known the proposed solution procedure is simple and direct five numerical examples are illustrated to demonstrate the feasibility and effectiveness of the proposed method

homotopic residual correction processes we present and analyze homotopic continuation residual correction algorithms for the computation of matrix inverses for complex indefinite hermitian input matrices our homotopic methods substantially accelerate the known nonhomotopic algorithms unlike the nonhomotopic case our algorithms require no pre estimation of the smallest singular value of an input matrix furthermore we guarantee rapid convergence to the inverses of well conditioned structured matrices even where no good initial approximation is available in particular we yield the inverse of a well conditioned n x n matrix with a structure of toeplitz hankel type in o n log 3 n flops for a large class of input matrices our methods can be extended to computing numerically the generalized inverses our numerical experiments confirm the validity of our analysis and the efficiency of the presented algorithms for well conditioned input matrices and furnished us with the proper values of the parameters that define our algorithms

a two step inexact newton chebyshev like method for inverse eigenvalue problems abstract a two step inexact newton chebyshev like method is proposed to solve inverse eigenvalue problems unlike general newton type methods which need to invert the jacobian matrix that may lead to an unexpected instability the proposed method can guarantee the numerical stability by exploiting the chebyshev method to approximate the inverse of the jacobian matrix theoretically we prove that the proposed method converges cubically numerical examples are given to demonstrate the effectiveness of our method

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

on the estimation of the boundary temperature on a sphere from measurements at its center abstract an improperly posed inverse heat conduction problem with radial symmetry is stabilized by reconstructing a mollified image of the unknowns strict error bounds are derived and after introducing certain inverse kernels the numerical problem is solved with an absolute minimum of computation

chebyshev type methods and preconditioning techniques recently a newton s iterative method is attracting more and more attention from various fields of science and engineering this method is generally quadratically convergent in this paper some chebyshev type methods with the third order convergence are analyzed in detail and used to compute approximate inverse preconditioners for solving the linear system ax b theoretic analysis and numerical experiments show that chebyshev s method is more effective than newton s one in the case of constructing approximate inverse preconditioners

third order iterative methods under kantorovich conditions we study a class of third order iterative methods for nonlinear equations on banach spaces a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found though in general these methods are not very extended due to their computational costs we will show some examples in which they are competitive and even cheaper than other simpler methods we center our analysis in both analytic and computational aspects

a geometric construction of iterative functions of order three to solve nonlinear equations in this paper we consider a geometric construction of iteration functions of order three to develop cubically convergent iterative methods for solving nonlinear equations this construction can be applied to any iteration function of order two to develop an iteration function of order three some examples are given of deriving several third order iteration methods and several numerical results follow to illustrate the performance of the derived methods

stair matrices and their generalizations with applications to iterative methods i a generalization of the successive overrelaxation method stair matrices and their generalizations are introduced some properties of the matrices are presented like triangular matrices this class of matrices provides bases of matrix splittings for iterative methods a remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation in particular a generalization of the successive overrelaxation sor method is introduced the sor theory on determination of the optimal parameter is extended to the generalized method to include a wide class of matrices the asymptotic rate of convergence of the new method is derived for hermitian positive definite matrices using bounds of the eigenvalues of jacobi matrices and numerical radius finally numerical tests are presented to corroborate the obtained results

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and d c c a the long range cross correlation exponent respectively described by the dfa and dcca methods this relationship will be accomplished theoretically by differentiating the dcca cross correlation coefficient d c c a n also for some specific times series we apply this theory in order to establish its validity

singularity wielandt s lemma and singular values in this study some upper and lower bounds for singular values of a general complex matrix are investigated according to singularity and wielandt s lemma of matrices especially some relationships between the singular values of the matrix a and its block norm matrix are established based on these relationships one may obtain the effective estimates for the singular values of large matrices by using the lower dimension norm matrices in addition a small error in piazza 2002 g piazza t politi an upper bound for the condition number of a matrix in spectral norm j comput appl math 143 1 2002 141 144 is also corrected some numerical experiments on saddle point problems show that these results are simple and sharp under suitable conditions