Browsing by Author "Iyer, Manjula A."

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    Algorithm XXX: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data
    Thacker, William I.; Zhang, Jingwei; Watson, Layne T.; Birch, Jeffrey B.; Iyer, Manjula A.; Berry, Michael W. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2009)
    Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.
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    Note on the Effectiveness OF Stochastic Optimization Algorithms for Robust Design
    Iyer, Manjula A.; Phillips, Rhonda D.; Trosset, Michael W.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2008-05-01)
    Robust design optimization (RDO) uses statistical decision theory and optimization techniques to optimize a design over a range of uncertainty (introduced by the manufacturing process and unintended uses). Since engineering ob jective functions tend to be costly to evaluate and prohibitively expensive to integrate (required within RDO), surrogates are introduced to allow the use of traditional optimization methods to find solutions. This paper explores the suitability of radically different (deterministic and stochastic) optimization methods to solve prototypical robust design problems. The algorithms include a genetic algorithm using a penalty function formulation, the simultaneous perturbation stochastic approximation (SPSA) method, and two gradient-based constrained nonlinear optimizers (method of feasible directions and sequential quadratic programming). The results show that the fully deterministic standard optimization algorithms are consistently more accurate, consistently more likely to terminate at feasible points, and consistently considerably less expensive than the fully nondeterministic algorithms.