8 results
Search Results
2. Deflated BiCG with an Application to Model Reduction.
- Author
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Meng, Jing, Zhu, Pei-Yong, and Li, Hou-Biao
- Subjects
- *
CONJUGATE gradient methods , *MATHEMATICAL simplification , *MATHEMATICAL sequences , *LINEAR systems , *ALGORITHMS , *APPROXIMATION theory - Abstract
Most calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right invariant subspaces inexpensively via small descenting direction vectors found by subsequent runs of deflated BiCG and then derives the deflated subspaces for the next pair of dual linear systems. This process leads to faster convergence for the next pair of systems. Numerical examples illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
3. Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning.
- Author
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Bergamaschi, Luca, Martínez, Angeles, and Pini, Giorgio
- Subjects
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RAYLEIGH quotient , *MATHEMATICAL optimization , *EIGENVALUES , *ALGORITHMS , *SYMMETRIC matrices , *APPROXIMATION theory , *MATHEMATICAL models , *CONJUGATE gradient methods - Abstract
The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse- approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
4. Solving a system of nonlinear integral equations by an RBF network
- Author
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Golbabai, A., Mammadov, M., and Seifollahi, S.
- Subjects
- *
RADIAL basis functions , *APPROXIMATION theory , *MATHEMATICAL optimization , *ALGORITHMS , *CONJUGATE gradient methods , *NEWTON-Raphson method - Abstract
Abstract: In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to update the weights of RBFN is studied in solving systems of nonlinear integral equations. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
5. An Improved Quasi-Static Finite-Difference Scheme for Induced Field Evaluation Based on the Biconjugate Gradient Method.
- Author
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Hua Wang, Feng Liu, Trakic, Adnan, and Crozier, Stuart
- Subjects
- *
CONJUGATE gradient methods , *MEDICAL imaging systems , *APPROXIMATION theory , *MEDICAL care , *MAGNETIC resonance imaging , *ALGORITHMS , *ELLIPSOIDS - Abstract
This paper presents a biconjugate gradient (BiCG) method that can significantly improve the performance of the quasi-static finite-difference scheme, which has been widely used to model field induction phenomena in voxel phantoms. The proposed BiCG method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional iterative, successive overrelaxation algorithm. The scheme has been validated against other known solutions on a lossy, multilayered ellipsoid phantom excited by an ideal coil loop. The wide application capability and computational performance of the BiCG method is demonstrated by modeling the exposure of MRI healthcare workers to fields produced by pulsed field gradients. This is an important topic of research in light of the Physical Agents Directive 2904/40/EC because a variety of realistic operator postures near the bore entrance of an MRI system are modeled. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
6. Gradient Pursuits.
- Author
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Blumensath, Thomas and Davies, Mike E.
- Subjects
- *
ALGORITHMS , *APPROXIMATION theory , *FUNCTIONAL analysis , *MATHEMATICAL functions , *CONJUGATE gradient methods , *NUMERICAL solutions to equations - Abstract
Sparse signal approximations have become a fundamental tool in signal processing with wide-ranging applications from source separation to signal acquisition. The ever-growing number of possible applications and, in particular, the ever-increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of fast and efficient algorithms has become paramount. Recently, very fast algorithms have been developed to solve convex optimization problems that are often used to approximate the sparse approximation problem; however, it has also been shown, that in certain circumstances, greedy strategies, such as orthogonal matching pursuit, can have better performance than the convex methods. In this paper, improvements to greedy strategies are proposed and algorithms are developed that approximate orthogonal matching pursuit with computational requirements more akin to matching pursuit. Three different directional optimization schemes based on the gradient, the conjugate gradient, and an approximation to the conjugate gradient are discussed, respectively. It is shown that the conjugate gradient update leads to a novel implementation of orthogonal matching pursuit, while the gradient-based approach as well as the approximate conjugate gradient methods both lead to fast approximations to orthogonal matching pursuit, with the approximate conjugate gradient method being superior to the gradient method. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
7. A Penalized Linear and Nonlinear Combined Conjugate GradientMethod for the Reconstruction of Fluorescence Molecular Tomography.
- Author
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Shang Shang, Jing Bai, Xiaolei Song, HongkaiWang, and Lau, Jaclyn
- Subjects
- *
FLUORESCENCE , *TOMOGRAPHY , *CONJUGATE gradient methods , *APPROXIMATION theory , *ALGORITHMS - Abstract
Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
8. A Control-Theoretic Approach to the Design of Zero Finding Numerical Methods.
- Author
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Bhaya, Amit and Kaszkurewicz, Eugenius
- Subjects
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NUMERICAL solutions to equations , *NUMERICAL analysis , *APPROXIMATION theory , *NONLINEAR differential equations , *DIFFERENTIAL equations , *LYAPUNOV functions , *NEWTON-Raphson method , *CONJUGATE gradient methods , *ALGORITHMS - Abstract
In this paper, it is shown how standard iterative methods for solving linear and nonlinear equations can be designed from the point of view of control. Appropriate choices of control Lyapunov functions (CLFs) lead to both continuous and discrete-time versions of the Newton-Raphson and conjugate gradient algorithms as well as new variants. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
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