a lanczos type method for multiple starting vectors given a square matrix and single right and left starting vectors the classical nonsymmetric lanczos process generates two sequences of bior thogonal basis vectors for the right and left krylov subspaces induced by the given matrix and vectors in this paper we propose a lanczos type algorithm that extends the classical lanczos process for single starting vectors to mul tiple starting vectors given a square matrix and two blocks of right and left starting vectors the algorithm generates two sequences of biorthogonal basis vectors for the right and left block krylov subspaces induced by the given data the algorithm can handle the most general case of right and left start ing blocks of arbitrary sizes while all previously proposed extensions of the lanczos process are restricted to right and left starting blocks of identical sizes other features of our algorithm include a built in deation procedure to detect and delete linearly dependent vectors in the block krylov sequences and the option to employ look ahead to remedy the potential breakdowns that may occur in nonsymmetric lanczos type methods

a generalized point process model for rainfall this paper further develops a stochastic model for rainfall at a single site in which storms arrive in a poisson process each storm generating a cluster of rain cells with each cell having a random duration and a random intensity the model is generalized by allowing each generated cell to be of n types the duration of each cell is an exponential random variable that has parameter dependent on the cell type the distribution of cell intensity is also dependent on the cell type so that the generalized model provides a correlation between the intensities and durations of the generated rain cells the case for two cell types is considered in some detail the cells are categorized as either heavy or light9 where the heavy cells have a shorter expected lifetime than the light cells which agrees with observational studies on precipitation fields properties are derived and used to fit the model to rainfall data at a single site the adequacy of fit is assessed by considering properties not used in the fitting procedure but which are of interest in applications e g extreme values further properties are derived which enable the model to be fitted to multi site rainfall data

lanczos algorithm for the quadratic eigenvalue problem in engineering applications abstract a new approach of employing the lanczos two sided recursion to solve the quadratic eigenvalue problem is presented the methodology employed retains the n order quadratic problems as posed without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenvalue problem of order 2n pursuing the concept of finding a characteristic matrix to yield an eigenvalue square matrix the lanczos recursion has been devised to solve the quadratic eigenvalue problem appropriate proofs showing the lanczos biorthogonal transformation are included the example problems presented validate the algorithm and show the effectiveness of the method for large quadratic eigenproblems

a comparison of stochastic models for spatial rainfall downscaling 1 we explore the performance of three types of stochastic models used for spatial rainfall downscaling and assess their ability to reproduce the statistics of precipitation fields observed during the gate radar experiment we consider a bounded multifractal cascade an autoregressive linear process passed through a nonlinear static filter sometimes called a meta gaussian model and a model based on the presence of individual rainfall cells with power law profile as test statistics we use the low order moments of the amplitude distribution the distribution of generalized fractal dimensions the generalized scaling exponents the slope of the power spectrum and the properties of the spatial autocorrelation the results of the analysis indicate that all models provide on average a satisfactory representation of the statistical properties of the gate rainfall fields including the anomalous scaling behavior with a slightly better performance of the model based on individual rainfall cells all models however display large scatter in the field to field comparison with the data these results indicate that data analysis alone does not allow at the moment for preferring one downscaling approach over another

practical use of analytically derived runoff models based on rainfall point processes this work reports on the practical usage of the four stochastic rainfall runoff models introduced by bierkens and puente 1990 these models which are lumped in space were analytically derived combining two rainfall point process models with two simple runoff parameterizations the rainfall models employ rectangular pulses with poisson prp and neyman scott nsrp arrivals respectively the runoff models route individual rainfall pulses via linear reservoirs one runoff parameterization accounts for surface runoff by using a single linear reservoir slr the other model considers both surface and groundwater runoff employing two linear reservoirs in parallel plr all four representations were tested on two catchments located in the netherlands and colombia emphasis was placed on the models ability to 1 give stable parameter values for data sets at alternative averaging aggregation lengths consistency and 2 preserve historical statistics at alternative averaging lengths when using parameters found from data at other averaging scales robustness results show that the use of alternative rainfall models may have little effect on runoff performance specifically the nsrp model resulted in more robust runoff behavior than the prp model only when combined to the slr parameterization the type of model used to route individual rainfall pulses was found to be important runoff representations containing the plr component were found more robust than those having the slr model

exact travelling wave solutions for the generalized nonlinear schrodinger gnls equation with a source by extended tanh coth sine cosine and exp function methods the capability of extended tanh coth sine cosine and exp function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed in this study the generalized nonlinear schrodinger gnls equation is solved by three different methods to obtain the single soliton solutions for the equation the extended tanh coth and sine cosine methods are used furthermore for this nonlinear evolution equation the exp function method is applied to derive various travelling wave solution results show that while the first two procedures easily provide a concise solution the exp function method provides a powerful mathematical means for solving nonlinear evolution equations in mathematical physics

nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations we propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the ablowitz kaup newell segur akns and the kaup newell classes based on the simple idea of dimensional analysis and detecting the building blocks of the lax pair along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the akns family e g the korteweg de vries kdv the modified kdv the nonlinear schrodinger and the sine gordon equation showing thus a twofold universality of the recently found deformation for the kdv equation a karsu et al j math phys 49 073516 2008

an envelope solitary wave solution for a generalized nonlinear schrodinger equation we derive an envelope solitary wave solution for the following generalized nonlinear schrodinger equation ut ia2uxx a3uxxx ib mod u mod 2u b1 mod u mod 2u x by gauge transformation

continuum design sensitivity of transient responses using ritz and mode acceleration methods in this paper a unified continuum based sizing design sensitivity analysis method is developed for the transient dynamic response of built up structures using the direct differentiation method the variational equation of the built up structure is differentiate d with respect to the design variable to obtain a variational design sensitivity equation of the transient response the same finite element analysis model that is used to obtain an approximate solution of the variational equation of the built up structure is also used to obtain an approximate solution of the variational design sensitivity equation for large size built up structures the same superposition method is used both to reduce the dimension of the matrix equation of the built up structure and also to reduce the dimension of the design sensitivity equation the continuum based design sensitivity analysis method can be implemented outside established finite element analysis codes using postprocessing data since it does not require derivatives of the stiffness damping and mass matrices moreover the method is efficient since it does not require derivatives of basis vectors either the ritz or mode acceleration method is used to further improve accuracy and efficiency of both analysis and sensitivity results an example with damping shows that accurate design sensitivity of pointwise transient displacements is obtained using only 10 of basis vectors this example indicates that in the continuum based design sensitivity analysis method the same basis vectors that are used for analysis of the built up structure are suitable for analysis of the design sensitivity equation

envelope exact solutions for the generalized nonlinear schrodinger equation with a source in this letter the generalized nonlinear schrodinger gnls equation phase locked a source ei t is investigated firstly we reduce this equation to a second order non homogeneous nonlinear ordinary differential equation via a plane wave transformation and some constraint conditions then we use some fractional transformations to study exact solutions in obtaining the gnls equation as a consequence many types of exact solutions are deduced such as envelope rational solutions envelope periodic wave solutions envelope solitary wave solutions and envelope doubly periodic solutions similarly the corresponding exact solutions can also be obtained for the hirota type gnls equation with a source and their combined equation

computational enhancement of an unsymmetric block lanczos algorithm an unsymmetric block lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and or repeated or closely spaced eigenvalues in the algorithm development the right and left lanczos vectors are all theoretically biorthogonal to each other however these vectors may lose the biorthogonality owing to cancellation and roundoff errors for the unsymmetric case there can be a breakdown even without numerical errors this paper describes computational techniques which have led to a robust unsymmetric block lanczos algorithm

the modified kdv equation with variable coefficients exact uni bi variable travelling wave like solutions in this paper the modified korteweg de vries mkdv equation with variable coefficients vc mkdv equation is investigated via two kinds of approaches and symbolic computation on the one hand we firstly reduce the vc mkdv equation to a second order nonlinear nonhomogeneous ode using travelling wave like similarity transformation and then we obtain its many types of exact fractional solutions with one travelling wave like variable by applying some fractional transformations to the obtained nonlinear ode on the other hand we reduce the vc mkdv equation to two nonlinear pdes with variable coefficients using the anti tangent and anti hypertangent function transformations respectively and then we given its many types of exact solutions with two different travelling wave like variables by studying the obtained nonlinear pde with variable coefficients c 2008 elsevier inc all rights reserved

on exact solitary wave solutions of the nonlinear schrodinger equation with a source we use a fractional transformation to connect the travelling wave solutions of the nonlinear schrodinger equation nlse phase locked with a source to the elliptic equations satisfying f af f3 0 the solutions are necessarily of rational form containing both trigonometric and hyperbolic types as special cases bright and dark solitons as well as singular solitons are obtained in a suitable range of parameter values

structural dynamics analysis using an unsymmetric block lanczos algorithm this paper describes the way in which an unsymmetric block lanczos algorithm can be employed for approximate eigensolutions or dynamic response solutions for large systems having arbitrary damping and or repeated or closely spaced eigenvalues to reduce a square unsymmetric matrix which may have repeated eigenvalues to block tridiagonal form an unsymmetric block lanczos algorithm is developed right and left lanczos vectors generated by the reduction process are employed to define the reduced order model based on a discrete analytical model of general linear time invariant dynamic systems a special type of starting vector is also introduced which automatically includes the static displacement this reduced order model is employed to compute approximate eigenvalues vectors and dynamic responses of the original system to verify the proposed algorithm examples of an 8 dof beam rotor system are provided for eigensolutions and dynamic responses due to step and random external forces these examples showed promising results indicating that the proposed algorithm is worthy of further study

a generalized spatial temporal model of rainfall based on a clustered point process the objective in this paper is to present and fit a relatively simple stochastic spatial temporal model of rainfall in which the arrival times of rain cells occur in a clustered point process in the x y plane rain cells are represented as discs each disc having a random radius the locations of the disc centres being given by a two dimensional poisson process the intensity of each cell is a random variable that remains constant over the area of the disc and throughout the lifetime of the cell the lifetime being an exponential random variable the cells are randomly classified from 1 to n with different parameters for the different cell types so that the random variables of an arbitrary cell e g radius and intensity are correlated multi site second order properties are derived and used to fit the model to hourly rainfall data taken from six sites in the thames basin uk

a subspace iteration algorithm for the eigensolution of large structures subject to non classical viscous damping reference lmaf article 2000 002view record in web of science record created on 2005 09 14 modified on 2017 05 10

an improved generalized f expansion method and its applications an improved generalized f expansion method is proposed to seek exact solutions of nonlinear evolution equations with the aid of symbolic computation we choose the generalized nonlinear schrodinger equation with a source to illustrate the validity and advantages of the proposed method many new and more general non travelling wave solutions are obtained including single and combined non degenerate jacobi elliptic function solutions solitons like solutions trigonometric function solutions and rational solutions the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in physics

further developments of the neyman scott clustered point process for modeling rainfall this paper provides some useful results for modeling rainfall it extends work on the neyman scott cluster model for simulating rainfall time series several important properties have previously been found for the model for example the expectation and variance of the amount of rain captured in an arbitrary time interval rodriguez iturbe et al 1987a in this paper additional properties are derived such as the probability of an arbitrary interval of any chosen length being dry in applications this is a desirable property to have and is often used for fitting stochastic rainfall models to field data the model is currently being used in rainfall time series research directed toward improving sewage systems in the united kingdom to illustrate the model s performance an example is given where the model is fitted to 10 years of hourly data taken from blackpool england

controlling temporal solitary waves in the generalized inhomogeneous coupled nonlinear schrodinger equations with varying source terms in this paper we study the families of solitary wave solutions to the inhomogeneous coupled nonlinear schrodinger equations with space and time modulated coefficients and source terms by means of the similarity reduction method and mobius transformations many types of novel temporal solitary wave solutions of this nonlinear dynamical system are analytically found under some constraint conditions such as the bright bright bright dark dark dark periodic periodic w shaped and rational wave solutions in particular we find that the localized rational type solutions can exhibit both bright bright and bright dark wave profiles by choosing different families of free parameters moreover we analyze the relationships among the group velocity dispersion profiles gain or loss distributions external potentials and inhomogeneous source profiles which provide the necessary constraint conditions to control the emerging wave dynamics finally a series of numerical simulations are performed to show the ro

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

the lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems many powerful methods for solving systems of equations can be regarded as projection methods most of the projection methods known for solving linear systems are orthogonal projection methods but little attention has been given to the class of nonorthogonal or oblique projection methods which is particularly attractive for large nonsymmetric systems the purpose of the paper is to present some methods in the general setting of oblique projection methods and to give some theoretical results some experiments comparing the various algorithms are reported

evaluation of cluster based rectangular pulses point process models for rainfall this technical note presents a comparison of cluster based point rainfall models using the historical hourly rainfall data observed between 1949 and 1976 at denver colorado the denver data are used to analyze the performance of three classes of models namely the bartlett lewis model the geometric neyman scott model and the poisson neyman scott model the original formulation of the structure of each model as well as the modified description developed in order to improve the zero depth probability is considered in this study rodriguez iturbe et al 1987a concluded that it is unlikely that empirical analysis of rainfall data can be used to choose between the bartlett lewis model and the neyman scott model in a subsequent paper rodriguez iturbe et al 1987b argued that the choice of the distribution of the number of cells per storm for the neyman scott model either geometric or poisson has no general bias effect on the stochastic structure some investigators e g burlando and rosso 1991 however reported results contradictory to those of the previous authors in light of these observations this note investigates the performance of the cluster based models for the denver data the geometric neyman scott model yields better results compared to the poisson neyman scott model moreover the bartlett lewis model is shown to be very sensitive to the sets of moment equations used in the parameter estimation this sensitivity is not observed in the neyman scott scheme and is believed to be a drawback for applying the bartlett lewis model in hydrologic simulation studies

a comparative copula based bivariate frequency analysis of observed and simulated storm events a case study on bartlett lewis modeled rainfall 1 because of a lack of historical rainfall time series of considerable length one often has to rely on simulated rainfall time series e g in the design of hydraulic structures one way to simulate such time series is by means of stochastic point process rainfall models such as the bartlett lewis type of model for the evaluation of model performance with a focus on the reproduction of extreme rainfall events often a univariate extreme value analysis is performed recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models in this study a copula based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms first this study performs an analysis of several storm variables which indicates a problem with the modeling of the temporal structure of rainfall by the models thereafter the bivariate frequency analysis of storms defined by their duration and volume illustrates the underestimation and overestimation of the return period of the storms simulated by the models which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume the difference in the degree of association between the latter and a different mean storm interarrival time the proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made

a space time neyman scott model of rainfall empirical analysis of extremes 1 a spatial temporal model of rainfall based on a neyman scott stochastic point process is fitted to hourly data taken from nine sites in the arno basin italy the stochastic model is an extension of the temporal neyman scott rectangular pulses model into two dimensional space and introduces a further parameter into the model in the model storms arrive in a poisson process where each storm consists of discs representing rain cells with centers distributed over an area according to a spatial poisson process the cells have a random radius lifetime and intensity with the intensity remaining constant over the area of the disc and cell lifetime a fitting procedure is proposed which couples the results obtained in two preceding papers the second order properties of the spatial temporal model and the third moment function of the single site model cowpertwait 1995 1998 the model is validated by comparing extreme historical hourly data and equivalent data simulated using the fitted spatial temporal model these comparisons are made using a regional frequency analysis based on l moments and log log plots of the upper distribution tail the results indicate that the model is able to preserve regional extremes and support the use of the model in hydrological applications

block krylov subspace methods for approximating the linear combination of ź functions arising in exponential integrators in this paper we present numerical methods for computing the matrix functions arising in exponential integrators the matrix functions are the linear combination of the form j 0 p j a b j where j is related to exponential function by reducing the corresponding systems of linear odes with polynomial inhomogeneity based on block krylov subspace methods two effective exponentials of low dimension matrix are derived to approximate the objective functions some useful a posteriori error estimates are established the algorithms can be combined with time stepping strategy to satisfy the accuracy requirements under a moderate dimension of the block krylov subspace several numerical experiments are presented to demonstrate the efficiency of the methods

the lanczos algorithm applied to unsymmetric generalized eigenvalue problem application of the two sided lanczos recursion to the unsymmetric generalized eigenvalue problem is presented the system matrices are real and unsymmetric therefore the recursions are performed in real arithmetic and complex arithmetic is employed in the qr algorithm used to extract the eigenvalues of the transformed tridiagonal matrix the biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in appendices issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed the example problems solved demonstrate the working of the algorithm in extracting the complex and or real eignevalues of an unsymmetric system of matrices also the algorithm is applied to extract a few of the eigenvalues of a large fluid structure interaction problem and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature

optimization of large structures subjected to dynamic loads with the multiplier method the multiplier method for optimization of large scale mechanical and structural systems subjected to dynamic loads is investigated a large scale dynamic response optimization problem is formulated and solved in several alternate ways using the first and second order forms of the equations of motion results are compared with those obtained with the sequential quadratic programming algorithm a primal method in all the cases investigated the multiplier algorithm is more efficient than the primal method therefore it is concluded that the multiplier method is more appropriate for dynamic response optimization of large scale problems