Abstract: In this paper, we present preconditioned generalized
accelerated overrelaxation (GAOR) methods for solving certain
nonsingular linear system. We compare the spectral radii of the
iteration matrices of the preconditioned and the original methods. The
comparison results show that the preconditioned GAOR methods
converge faster than the GAOR method whenever the GAOR method
is convergent. Finally, we give two numerical examples to confirm our
theoretical results.
Abstract: In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.
Abstract: In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.
Abstract: In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method
with the presented new preconditioner.
Abstract: In this paper, the backward MPSD (Modified Preconditioned
Simultaneous Displacement) iterative matrix is firstly
proposed. The relationship of eigenvalues between the backward
MPSD iterative matrix and backward Jacobi iterative matrix for block
p-cyclic case is obtained, which improves and refines the results in
the corresponding references.
Abstract: In this paper, we present the preconditioned mixed-type
splitting iterative method for solving the linear systems, Ax = b,
where A is a Z-matrix. And we give some comparison theorems
to show that the convergence rate of the preconditioned mixed-type
splitting iterative method is faster than that of the mixed-type splitting
iterative method. Finally, we give a numerical example to illustrate
our results.
Abstract: An inflation–extension test with human vena cava
inferior was performed with the aim to fit a material model. The vein
was modeled as a thick–walled tube loaded by internal pressure and
axial force. The material was assumed to be an incompressible
hyperelastic fiber reinforced continuum. Fibers are supposed to be
arranged in two families of anti–symmetric helices. Considered
anisotropy corresponds to local orthotropy. Used strain energy
density function was based on a concept of limiting strain
extensibility. The pressurization was comprised by four pre–cycles
under physiological venous loading (0 – 4kPa) and four cycles under
nonphysiological loading (0 – 21kPa). Each overloading cycle was
performed with different value of axial weight. Overloading data
were used in regression analysis to fit material model. Considered
model did not fit experimental data so good. Especially predictions
of axial force failed. It was hypothesized that due to
nonphysiological values of loading pressure and different values of
axial weight the material was not preconditioned enough and some
damage occurred inside the wall. A limiting fiber extensibility
parameter Jm was assumed to be in relation to supposed damage.
Each of overloading cycles was fitted separately with different values
of Jm. Other parameters were held the same. This approach turned out
to be successful. Variable value of Jm can describe changes in the
axial force – axial stretch response and satisfy pressure – radius
dependence simultaneously.
Abstract: Young patients suffering from Cerebral Palsy are
facing difficult choices concerning heavy surgeries. Diagnosis settled
by surgeons can be complex and on the other hand decision for
patient about getting or not such a surgery involves important
reflection effort. Proposed software combining prediction for
surgeries and post surgery kinematic values, and from 3D model
representing the patient is an innovative tool helpful for both patients
and medicine professionals. Beginning with analysis and
classification of kinematics values from Data Base extracted from
gait analysis in 3 separated clusters, it is possible to determine close
similarity between patients. Prediction surgery best adapted to
improve a patient gait is then determined by operating a suitable
preconditioned neural network. Finally, patient 3D modeling based
on kinematic values analysis, is animated thanks to post surgery
kinematic vectors characterizing the closest patient selected from
patients clustering.
Abstract: This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.
Abstract: In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.
Abstract: The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.
Abstract: This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.
Abstract: A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.
Abstract: The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.