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INTERNATIONAL "JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS", VOLUME 23, 2017. APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS. ORIGINAL PEER REVIEWED ARTICLES FROM AROUND THE WORLD.

Topics: APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS

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Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical perfection. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling--game theory, statistics,...

Topics: Computational Mathematics, Mathematical Modeling

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Professor George Anastassiou of U. Memphis

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Journal of Computational Analysis and Applications is an Applied Mathematics journal. Here are volumes 20, 21 of 2016. It is published by Eudoxus Press, LLC www.eudoxuspress.com A peer reviewed open access journal.

Topics: Applied Mathematics, Computational Mathematics

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VOLUMES OF: JOURNAL OF APPLIED FUNCTIONAL ANALYSIS, JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, AND JOURNAL OF CONCRETE AND APPLICABLE MATHEMATICS, 2004-2013

Topics: APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS

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GEORGE ANASTASSIOU

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JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, VOLUME 28, 2020.

Topics: APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS, ORIGINAL ARTICLES, PEER REVIEWED

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VOLUMES OF: JOURNAL OF APPLIED FUNCTIONAL ANALYSIS, JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, JOURNAL OF CONCRETE AND APPLICABLE MATHEMATICS

Topics: APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS, ORIGINAL RESEARCH IN MATH

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This is a PDF of Intelligent Mathematics Computational Analysis in English Language & script as authored by George A. Anastassiou. the book provides a rigorous mathematical theory used in Computational Analysis essential for applied mathematical subjects such as Computational complexity analysis and Theoretical computer science. I have no monetary benefits from this work & it is intended for non-commercial uses only.

Topics: Mathematics, Computational Mathematics, Analysis, Intelligent Mathematics Computational Analysis,...

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Pickover, Clifford A

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xvi, 394 pages, 10 unnumbered pages of plates : 24 cm

Topics: Computer graphics, Infographie, Computergrafik, Computergraphics, Chaos, Algoritmen,...

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1 online resource (xxv, 466 pages) :

Topics: Membranes, computational mathematics, Membranen, Bilayer lipid membranes -- Computer simulation,...

In an earlier paper (ZAMM 63, 1983, 21), J.P.Fink and W.C.Rheinboldt developed a priori local error estimates for the scalar-parameter case of the reduced basis method by considering the method in a differential-geometric setting. Here it is shown that an analogous setting can be used for the analysis of the method applied to problems with a multidimensional parameter vector and that this leads to a corresponding local error theory also in this general case.

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. We address the situation where a signal S is known to consist of N equispaced samples, of which only LN are available. This includes the case of equispaced data with gaps; if the ratio p=L/N is smaller than 1, the available data are typically non-equispaced samples, with little or no visible trace of the equispacing the full set of N samples. Then our algorithm reconstructs a near-optimal...

Topics: DTIC Archive, Zhou, Jing, PRINCETON UNIV NJ PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS, *FAST...

This paper presents a general existence and uniqueness theory for differential-alegebraic equations extending the well known ODE theory. Both local and global aspects are considered, and the definition of the index for nonlinear problems is elucidated. For the case of linear problems with constant coefficients the results are shown to provide an alternate treatment equivalent to the standard approach in terms of matrix pencils. Also, it is proved that general differential-algebraic equations...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Many iterative algorithms for the solution of large linear systems may be effectively vectorized only if the diagonal of the matrix is surrounded by a large band of zeroes, which is called the zero stretch. In this paper, a multicolor numbering technique is suggested for maximizing the zero stretch of irregularly sparse matrices. The technique, which is generalization of a known algorithm for regularly sparse matrices, executes in linear time, and produces a zero stretch approximately equal to...

Topics: DTIC Archive, Melhem, Rami G, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

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128 pages : 26 cm

Topics: Computer graphics, Infographie, Computer graphics, Computergrafik, Computergraphics, Computer...

New second- and third-order algorithms are presented for calculating translating and rotating steady-state solutions of the 2D incompressible Euler equations (which we call V-state). These are piecewise constant regions of vorticity and the contours bounding them are obtained by solving iteratively a nonlinear integro-differential equation. New limiting contours with corners are obtained and compared with local analytical solutions. The precise results correct mistakes for limiting contours...

Topics: DTIC Archive, Wu,H M, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Given two Banach spaces X and Y over K = R or C and a parameterized family A (mu) an element of L(X, Y) with mu an element of K, partial and algebraic multiplicities of any value mu sub 0 an element of K such that A (mu sub 0) if Fredholm with index zero are defined by the means of generalized Jordan chains. These notions are developed in close connection with bifurcation problems and we show that partial and algebraic multiplicities are not affected by Lyapunov-Schmidt reduction. Properties of...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

An algorithm is presented for the computation of the second fundamental tensor V of a Riemannian sub-manifold M of R superscript n. From V the Riemann curvature tensor of M is easily obtained. Moreover, V has a close relation to the second derivative of certain functionals on M which, in turn, provides a powerful new tool for the computational determination of multiple bifurcation directions. Frequently, in applications, the manifold M is defined implicitly as the zero set of a submersion F on...

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

The sensitivity of a solution of a parameterized equation F(z, lamda) = 0 with respect to the parameter vector lambda is usually defined as the change of the state z in dependence of lambda. In other words, for any solution expressible in the form (z(lambda), lambda) with some smooth function z = z(lambda) the sensitivity is the derivative Dz(lambda). Typically the solutions form a manifold M in the product of the state-space and the parameter space and this sensitivity is available only at...

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

A special class of self-timed networks is defined and two steps are suggested for the verification of any computation performed on networks in this class. First, a proof that the network is deadlock-free, and second, a verification of the results of the computation. In relation to the first step, an algebra of events is developed and used to prove that the liveness of any self-timed network is determined uniquely by its initial state. Moreover, a method is presented for the verification of...

Topics: DTIC Archive, Melhem,R G, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Partial Contents: On lacunary incomplete polynomials; Theorems of Stein-Rosenberg type. II. Optimal paths of relaxation in the complex plane; An extension to rational functions of a Theorem of J. L. Walsh on differences of interpolating polynomials; Theorems of Stein-Rosenberg type. III. The singular case; On the LU factorization of M-matrices. (kr)

Topics: DTIC Archive, Varga, Richard S, KENT STATE UNIV OH INST FOR COMPUTATIONAL MATHEMATICS, *REPORTS,...

This paper considers networks in which the execution time of local cycles depends on the input data. Typically, this may occur if the local cycles contain branching statements. Although data driven networks are self-synchronized, and hence, local cycles are allowed to have different execution times, it is not obvious that the execution of the entire network may benefit from the fast execution of some local cycles. More specifically, internal data conflict may force a potentially short local...

Topics: DTIC Archive, Melhem, Rami G, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

The problem of determining closed curves that are invariant under some given mapping arises in many applications and various numerical techniques have been proposed for the calculation of such invariant cycles. The authors refer here only to Doedel Iooss et al, Kevrekidis et al, Van Veldhuizen. Keywords: Differential equations; Vertices.

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

The aims of this project, as set out in the original proposal, may be summarized as follows: an investigation would be undertaken into the use of finite element methods for three-dimensional linear problems from potential theory and elasticity containing singularities and for nonlinear problems, particularly those involving the elasto-plastic deformation of three-dimensional solids. Special emphasis would be given to the forms of singularities in three-dimensional linear problems and the use...

Topics: DTIC Archive, Whiteman,J R, BRUNEL UNIV UXBRIDGE (ENGLAND) INST OF COMPUTATIONAL MATHEMATICS,...

Our primary objective is to use the wave-theoretic travel-time sensitivity kernel in order to study the effect of increasing range on the sensitivity of finite-frequency travel-time observables to sound-speed perturbations. A further objective is to compare wave-theoretic travel-time sensitivity kernels and Fresnel volumes associated with particular eigenrays, seeking connections between the ray-theoretic and wave-theoretic description of travel-time observables.

Topics: DTIC Archive, FOUNDATION FOR RESEARCH AND TECHNOLOGY-HELLAS HERAKLION CRETE (GREECE) INSTITUTE OF...

Earlier a new algorithm was developed for computing vertices of a simplicial triangulation of subsets of a p-dimensional manifold M defined as the solution of a parametrized nonlinear equation. The algorithm depends on a method for constructing a moving frame on these subsets of M. Here an overview of these two algorithms is given together with some numerical examples that illustrate their effectiveness. (Author)

Topics: DTIC Archive, Rheinboldt,Warner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

It comes as no surprise that the literature devoted to bifurcation problems involving symmetry draws from both analysis and group theory. However, it is more accurate to say that it draws from both analysis and group representation theory, the two being related through the notion of isotropy subgroup. Isotropy subgroups have been crucial to every work having some connection with bifurcation and symmetry. It is the aim of this paper to show that there are connections between bifurcation problems...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

We give sufficient condition for a C(1) submersion F : X - Y, X Y real Banach spaces, to be surjective with contractible fibers F(-1)(y). Roughly speaking, this condition interpolates two well-known but unrelated hypotheses coresponding to the two extreme cases: Hadanard's criterion when Y = X and F is a local diffeomorphism, and the Palais-Smale condition when Y = R. These results may be viewed as a global variant of the implicit function theorem, which unlike the local one does not require...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Under certain conditions (known as the Restricted Isometry Property or RIP) on the m x N matrix (where m N), vectors x included in R(sup N) that are sparse (i.e. have most of their entries equal to zero) can be recovered exactly from y := Phi-x even though Phi(inverse)(y) is typically an (N - m)- dimensional hyperplane; in addition x is then equal to the element in Phi(inverse)(y) of minimal L1-norm. This minimal element can be identified via linear programming algorithms. We study an...

Topics: DTIC Archive, PRINCETON UNIV NJ PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS, *CONVERGENCE,...

The authors considers large, sparse linear systems which result from the discretization of partial differential equations on regular and irregular domains, and he focuses on the application of the preconditioned conjugate gradient (PCCG) method to the solution of such systems. More specifically, the goal of this paper is the efficient implementation of the PCCG method on vector supercomputers. The contribution to the above goal is made by 1) the introduction of a data structure which way be...

Topics: DTIC Archive, Melhem,Rami, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Two 2-day workshops were held. These concentrated on MATLAB, which is a high-level computer language for scientific and engineering calculations. It is extremely useful for many exploratory investigations, and for problems that need efficient use of matrices. Some of the advantages of MATLAB over lower- level languages like FORTRAN are: (1) The essentials can be learned very easily - one day; (2) Programs tend to be short, easy to write and read; (3) MATLAB is interactive, which makes it easy...

Topics: DTIC Archive, Noble, Ben, BRUNEL UNIV UXBRIDGE (UNITED KINGDOM) INST OF COMPUTATIONAL MATHEMATICS,...

This represents the second Part of the report on NFEARS, the Nonlinear Finite Element Adaptive Research Solver developed jointly by the Universities of Maryland and Pittsburgh. This part constitutes the User's Manual for the system version 6. It was intended to describe all necessary aspects for running NFEARS successfully without requiring a detailed knowledge of the mathematical background given in Part I. However, the reader should be generally familiar with the aims and tasks of the program.

Topics: DTIC Archive, Mesztenyi, Charles K, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

This is a written version of a series of invited lectures on differential-algebraic systems of equations (DAEs) at the IVth SERC Numerical Analysis Summer School of Lancaster Univ. In line with the aims of the meeting these notes introduce some typical applications and basic properties of DAEs and then present an overview of recent, new existence theories for such systems based on differential geometric considerations and on a numerical approach derived from these theories. In the presentation...

Topics: DTIC Archive, Rheinboldt, W C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

A differential geometric approach for proving the existence and uniqueness of solutions of implicit differential algebraic equations is presented. It provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems. The differential algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

This report contains the quarterly reports from the PI as follows: 1 March - 31 May 2008 * 31 Oct - 31 Mar 2009 * 1 Mar - 30 May 2009 * 1 June - 31 Aug 2009 * 1 Jan - 31 March 2010 * 1 Apr - 30 June 2010 * 1 July - 30 Sep 2010

Topics: DTIC Archive, FOUNDATION FOR RESEARCH AND TECHNOLOGY-HELLAS HERAKLION CRETE (GREECE) INSTITUTE OF...

This represents the second Part of the report on NFEARS, the Nonlinear Finite Element Adaptive Research Solver developed jointly by the Universities of Maryland and Pittsburgh. This part constitutes the User's Manual for the system. It was intended to describe all necessary aspects for running NFEARS successfully without requiring a detailed knowledge of the mathematical background given in Part 1. However, the reader should be generally familiar with the aims and tasks of the program.

Topics: DTIC Archive, Mesztenyi, Charles K, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

In a previous publication an abstract model was developed for the specification of systollc networks and the verification of the correctness of their operation. The model was applied to the verification of the operation of four systollc networks that had been suggested in the literature. In this report, the authors extends this model to allow for networks with slightly more complicated types of computational cells, namely cells that have periodic memory or multiplexing capabilities.

Topics: DTIC Archive, Melhem,Rami, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Advances in Cryptology — EUROCRYPT ’99: International Conference on the Theory and Application of Cryptographic Techniques Prague, Czech Republic, May 2–6, 1999 Proceedings Author: Jacques Stern Published by Springer Berlin Heidelberg ISBN: 978-3-540-65889-4 DOI: 10.1007/3-540-48910-X Table of Contents: Cryptanalysis of RSA with Private Key d Less than N Cryptanalysis of Skipjack Reduced to 31 Rounds Using Impossible Differentials Software Performance of Universal Hash Functions Lower...

Topics: Computational complexity, Computer Communication Networks, Computer science, Computer...

Equilibrium problems for many physical systems are modelled by parameter dependent nonlinear equations F(z,lambda) =0. Under fairly general conditions the set of solutions (z, lambda) of this equation forms a differentiable manifold, and, typically in applications, interest centers not so much on computing a few solutions but rather on analysing the form and special features of this manifold. This paper identifies some of the sources of the errors which are necessarily arising in such a...

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Many applications lead to nonlinear, parameter dependent equations H(y,t) = y sub o, where H: Y x T yields Y, y sub o epsilon rge H, and the state space Y is infinite-dimensional while the parameter space T has finite dimension. The case dim T = 1 is of special interest in connection with continuation methods. For this case, a general theory is developed which provides for the existence of solution paths of a rather general class of such equations and of their finite-dimensional approximations,...

Topics: DTIC Archive, Fink,James P, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Differential-algebraic systems of equations (DAEs) arise in many areas of science and engineering. In particular, the equations of motion for a constrained mechanical systems considered in this volume are usually modelled as a second order DAE. In recent years the literature on the numerical solution of such systems has grown rapidly. However, up to now, existence theories for nonlinear DAEs are available only for a few selected classes of systems. The differential-geometric approach is based...

Topics: DTIC Archive, Potra, Florian A, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

This paper presents general techniques based on the theory of Fredholm operators for analyzing the solutions of parametrized nonlinear equations and their finite-dimensional approximations. In particular, it is shown how to obtain the existence of solution paths, both for a general class of nonlinear equations and for their discretizations, and to develop error estimates. Finally it is also shown that the results include existing results for mildly nonlinear problems. (Author)

Topics: DTIC Archive, Fink,James P, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

The multiplication of a matrix by a vector and the solution of triangular linear systems are the most demanding operations in the majority of iterative techniques for the solution of linear systems. Data-driven VLSI networks that perform these two operations, efficiently, for sparse matrices are introduced. In order to avoid computations that involve zero operands, the non-zero elements in a sparse matrix are organized in the form of non intersecting stripes, and only the elements within the...

Topics: DTIC Archive, Melhem, Rami, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Automatic generation of sequential and parallel programs can bring the power of modern computers to more engineers and scientists. The project investigated parallel code generation and automatic derivation of parallel finite element routines. Software packages GENCRAY, a code translator producing Cray Fortran, and PIER, a finite element code derivation system, have been constructed as research tools.

Topics: DTIC Archive, Wang, Paul S., KENT STATE UNIV OH INST FOR COMPUTATIONAL MATHEMATICS, *FINITE ELEMENT...

The stripe structures of stiffness matrices resulting from irregular domains covered by regular grids; are analysed. It is proved that the non-zero elements in these matrices may be covered by very few stripes, and that these stripes may be non-overlapping, if the nodes of the grids are numbered appropriately. The exact number of stripes, which is independent of the size of the problem, is derived for different types of grids, and different numbering schemes. The stripe structure of some...

Topics: DTIC Archive, Melhem, Rami, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

Implementation of the reduced basis method requires the choice of a subspace and a projector onto that subspace. For an arbitrarily chosen subspace-projector pair, existence of the true solution curve is not sufficient to guarantee the existence of the corresponding reduced basis solution curve. However, when the former curve exists, it has been shown that there are infinitely many subspace-projector pairings, each utilizing an arbitrarily selected subspace, under which the reduced basis...

Topics: DTIC Archive, Hall,Charles A, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Summarizes the work done studying the stability and scattering of translating V-state solutions of the Euler equations in two-dimensions. This is a computer simulation study using the method of contour dynamics, a new boundary-integral evolutionary method.

Topics: DTIC Archive, Zabusky,N J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS,...

This paper presents a mathematical model for systolic architectures for use in the verification of the operation of certain systolic networks. The I/O description of the global effect of the computations performed by the network are obtained by solving a particular system of difference equations. The verification technique is applied to four different systolic networks proposed in the literature. (Author)

Topics: DTIC Archive, Melhem,Rami G, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

Existence and uniqueness results are proved for initial value problems associated with linear, time-varying, differential-algebraic equations. The right-hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses . This approach also provides a satisfactory answer to the problem of inconsistent initial conditions of crucial importance for the physical applications. Furthermore, our theoretical results yield an efficient numerical...

Topics: DTIC Archive, Rabier, Patrick J, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...

The study of many equilibrium phenomena leads to non-linear equations which involve a number of intrinsic parameters. Interest then centers rarely on the determination of a few specific solutions of the equations for fixed parameter values but rather on an assessment of the behavior of these solutions under general variations of the parameters. For example, in structural analysis the parameters may characterize load points and load directions, material properties, geometrical data, etc. The set...

Topics: DTIC Archive, Rheinboldt, Werner C, PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND...