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13
Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
, 1993
"... The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to a ..."
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Cited by 439 (12 self)
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The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the tradeoff surface.
Combinatorial preconditioners for sparse, symmetric, diagonally dominant linear systems
, 1996
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The efficient evaluation of the hypergeometric function of a matrix argument
 Math. Comp
"... Abstract. We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the ..."
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Cited by 28 (10 self)
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Abstract. We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix. 1.
Accurate and efficient evaluation of Schur and Jack functions
 Math. Comp
, 2006
"... Abstract. We present new algorithms for computing the values of the Schur sλ(x1,x2,...,xn)andJackJ α λ (x1,x2,...,xn) functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data (xi,α>0) and run in time that is only linear in n. 1. ..."
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Cited by 7 (4 self)
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Abstract. We present new algorithms for computing the values of the Schur sλ(x1,x2,...,xn)andJackJ α λ (x1,x2,...,xn) functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data (xi,α>0) and run in time that is only linear in n. 1.
Accurate and efficient expression evaluation and linear algebra
, 2008
"... We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correc ..."
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Cited by 3 (0 self)
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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the socalled traditional model (TM), where the computed result of op(a, b), a binary operation like a + b, is given by op(a, b) ∗ (1 + δ) where all we know is that δ  ≤ε ≪ 1. Here ε is a constant also known as machine epsilon.
Implicit Standard Jacobi Gives High Relative Accuracy
, 2008
"... We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDX T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O(εκ(X)), where ε is the machin ..."
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Cited by 2 (0 self)
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We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDX T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O(εκ(X)), where ε is the machine precision and κ(X) ≡ ‖X‖2 · ‖X −1 ‖2 is the spectral condition number of X. The eigenvectors are also computed accurately in the appropriate sense. We believe that this is the first algorithm to compute accurate eigenvalues of symmetric (indefinite) matrices that respects and preserves the symmetry of the problem and uses only orthogonal transformations.
Composite Constructs For ObjectOriented Modeling
 Proc. Eurosim Simulation Congress
, 1995
"... Object orientation in modeling, i.e. the possibility to structure a model according to the objects present in the system under consideration, promotes reuse and simplifies maintenance. This paper is mainly devoted to composite language constructs, like matrix notation, multiple inheritance and gener ..."
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Cited by 1 (0 self)
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Object orientation in modeling, i.e. the possibility to structure a model according to the objects present in the system under consideration, promotes reuse and simplifies maintenance. This paper is mainly devoted to composite language constructs, like matrix notation, multiple inheritance and generic class parameters, that are introduced in order to further facilitate reuse and maintenance of models.
Elements of MATLAB
, 1988
"... this document were run on UNIX workstations; both a Sun 3/60 under the SunView window environment and a DECstation ..."
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this document were run on UNIX workstations; both a Sun 3/60 under the SunView window environment and a DECstation
Computer Graphics and Visualization
"... Introduction A large amount of data is produced with high performance scientific computing. The term, visualization for scientific computing, shortened to scientific visualization, was coined in 1986 and refers to the science or methodology of quickly and effectively displaying scientific data. The ..."
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Introduction A large amount of data is produced with high performance scientific computing. The term, visualization for scientific computing, shortened to scientific visualization, was coined in 1986 and refers to the science or methodology of quickly and effectively displaying scientific data. The goal of scientific visualization is to enhance scientific productivity by utilizing human visual perception and computer graphics techniques. Hence computer graphics has become an important part of scientific computing. A large number of software packages now exist to aid the scientist in developing graphical representations of his data. These packages include Matlab by MathWorks, Inc., IDL by Research Systems, Inc., and AVS by Stardent. In order to use these graphics effectively, some understanding of visual perception is needed. 1 This work has been supported by the National