Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 18 May 2022 22:48:25 GMT2022-05-18T22:48:25Z10891Splitting methods for constrained quadratic programs in data analysishttp://hdl.handle.net/11380/304917Titolo: Splitting methods for constrained quadratic programs in data analysis
Abstract: This paper is concerned with the numerical solution of a linearly constrained quadratic programming problem by methods that use a splitting of the objective matrix. We present an acceleration step for a general splitting algorithm and we establish the convergence of the resulting accelerated scheme. We report the results of numerical experiments arising in constrained bivariate interpolation to evaluate the efficiency of this acceleration technique for a particular splitting of the objective matrix and for the corresponding extrapolated form.
Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/11380/3049171996-01-01T00:00:00ZA two-stage iterative method for solving a weakly nonlinear parametrized systemhttp://hdl.handle.net/11380/305138Titolo: A two-stage iterative method for solving a weakly nonlinear parametrized system
Abstract: In this paper we consider a parametrized system of weakly nonlinear equations which corresponds to a nonlinear elliptic boundary-value problem with zero source, homogeneous boundary conditions and a positive parameter in the linear term. Positive solutions of this system are of interest to us. A characterization of this positive solution is given. Such a solution is determined by the Modified Newton-Arithmetic Mean method. This method is well suited for implementation on parallel computers. A theorem about the monotone convergence of the method is proved. An application of the method for solving a real practical problem related to the study of interacting populations is described.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/11380/3051382002-01-01T00:00:00ZError analysis of null space algorithm for linear equality constrained least squares problemshttp://hdl.handle.net/11380/612211Titolo: Error analysis of null space algorithm for linear equality constrained least squares problems
Abstract: The numerical stability of the null space method for linear least-squares problems with linear equality constraints is studied using a backward error analysis. A class of test problems is also considered in order to show experimentally the behaviour of the method.
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/11380/6122111994-01-01T00:00:00ZSplitting methods and parallel solution of constrained quadratic programshttp://hdl.handle.net/11380/593955Titolo: Splitting methods and parallel solution of constrained quadratic programs
Abstract: In this work the numerical solution of linearly constrained quadratic programming problems is examined. This problem arises in many applications and it forms a basis for some algorithms that solve variational inequalities formulating equilibrium problems. An attractive iterative scheme for solving constrained quadratic programs when the matrix of the objective function is large and sparse consists in transforming, by a splitting of the objective matrix, the original problem into a sequence of subproblems easier to solve. At each iteration the subproblem is formulated as a linear complementarity problem that can be solved by methods suited for implementation on multiprocessor system. We analyse two parallel iterative solvers from the theoretical and practical point of view. Results of numerical experiments carried out on Cray T3D are reported.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/5939551997-01-01T00:00:00ZOn the stability of the direct elimination method for equality constrained least squares problemshttp://hdl.handle.net/11380/305507Titolo: On the stability of the direct elimination method for equality constrained least squares problems
Abstract: A backward error analysis of the direct elimination method for linear equality constrained least squares problems is presented. It is proved that the solution computed by the method is the exact solution of a perturbed problem and bounds for data perturbations are given. The numerical stability of the method is related to the way in which the constraints are used to eliminate variables and these theoretical conclusions are confirmed by a numerical example.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11380/3055072000-01-01T00:00:00ZInner solvers for interior point methods for large scale nonlinear programminghttp://hdl.handle.net/11380/421269Titolo: Inner solvers for interior point methods for large scale nonlinear programming
Abstract: This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution.In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11380/4212692007-01-01T00:00:00ZThe Arithmetic Mean method for solving systems of nonlinear equations in finite differenceshttp://hdl.handle.net/11380/305912Titolo: The Arithmetic Mean method for solving systems of nonlinear equations in finite differences
Abstract: In this paper we consider the application of additive operator splitting methods for solving a finite difference nonlinear system of the form F(u) = (I - tau A(u))u - w = 0 generated by the discretization of two dimensional diffusion-convection problems with Neumann boundary conditions. Existence and uniqueness of a solution of this system has been proved under standard assumptions on the matrix A(u) and the source term w. Using the fact that the matrix A(u) can be decomposed into different splittings, we develop a nonlinear Arithmetic Mean method and a two-stage iterative method (a fixed-point-Arithmetic Mean method) for solving the system above. The convergence of these methods has been analyzed. Numerical experiments show that the fixed-point-Arithmetic Mean method is rapidly convergent when the diffusion coefficient is weakly nonlinear. (c) 2006 Elsevier Inc. All rights reserved.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/3059122006-01-01T00:00:00ZA note on the iterative solution of nonlinear steady state reaction diffusion problemshttp://hdl.handle.net/11380/741026Titolo: A note on the iterative solution of nonlinear steady state reaction diffusion problems
Abstract: This report concerns with the numerical solution of nonlinear reaction diffusion equations at the steady state in a two dimensional bounded domain supplemented by suitable boundary conditions. When we use finite differences or finite element discretizations, the nonlinear diffusion equation subject to Dirichlet boundary conditions can be transcribed into a nonlinear system of algebraic equations. In the case of finite differences, the matrix that arises from the discretization of the diffusion (and/or convection) term satisfies properties of monotonicity.This report is divided into two parts (chapters): the first part deals with the solution of a weakly nonlinear reaction diffusion equation while in the second part, the solution of a strongly nonlinear reaction diffusion equation is computed by an iterative procedure that “lags” the diffusion term. This procedure is called Lagged Diffusivity Functional Iteration (LDFI)–procedure.In the first part the weakly nonlinear algebraic system arising from the discretization is solved by a simplified Newton method comkbined with the Arithmetic Mean method that is an iterative method, suited for parallel computers, for the solution of large sparse linear systems. This inner-outer iteration process gives a two-stage iterative method.Results concerning the global and monotone convergence for the two-stage iterative method have been reported. Furthermore, numerical experiments show the efficiency of the two-stage iterative method, especially for a dominant convection term, confirming the well known results for the linear case.In the second part the LDFI-procedure for the solution of the strongly nonlinear reaction diffusion equation is analyzed. A model problem is considered and a finite difference discretization for that model problem is described. Furthermore, in the report, properties of the finite difference operator are proved. Then, sufficient conditions for the convergence of the LDFI-procedure are given. At each stage of the LDFI-procedure a weakly nonlinear algebraic system has to be solved and the simplified Newton-Arithmetic Mean method is used. Numerical studies show the efficiency for different test functions of the LDFI-procedure combined with the simplified Newton-Arithmetic Mean method. Better result are obtained for dominant convection coefficients according with the linear and the weakly nonlinear cases.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/7410262010-01-01T00:00:00ZThe two-stage arithmetic mean methodhttp://hdl.handle.net/11380/303962Titolo: The two-stage arithmetic mean method
Abstract: In several recent works, the Arithmetic Mean Method for solving large sparse linear systems has been introduced and analysed. Each iteration of this method consists of solving two independent systems. When we obtain two approximate solutions of these systems by a prefixed number of steps of an iterative scheme, we generate an inner/outer procedure, called Two-Stage Arithmetic Mean Method. General convergence theorems are proved for M-matrices and for symmetric positive definite matrices. In particular, we analyze a version of Two-Stage Arithmetic Mean Method for T(q, r) matrices, deriving the convergence conditions. The method is well suited for implementation on a parallel computer. Numerical experiments carried out on Cray-T3D permits to evaluate the effectiveness of the Two-Stage Arithmetic Mean Method.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/3039621997-01-01T00:00:00ZThe Newton-arithmetic mean method for the solution of systems of nonlinear equationshttp://hdl.handle.net/11380/303571Titolo: The Newton-arithmetic mean method for the solution of systems of nonlinear equations
Abstract: This paper is concerned with the development of the Newton-arithmetic mean method for large systems of nonlinear equations with block-partitioned Jacobian matrix. This method is well suited for implementation on a parallel computer; its degree of decomposition is very high. The convergence of the method is analysed for the class of systems whose Jacobian matrix satisfies an affine invariant Lipschitz condition. An estimation of the radius of the attraction ball is given. Special attention is reserved to the case of weakly nonlinear systems. A numerical example highlights some peculiar properties of the method. (C) 2002 Elsevier Science Inc. All rights reserved.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/3035712003-01-01T00:00:00Z