68,208 research outputs found
Implementation of a continuation method for nonlinear complementarity problems via normal maps
Ankara : Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references.In this thesis, a continuation method for nonlinear complementarity
problems via normal maps that is developed by Chen, Harker and Pinar [8]
is implemented. This continuation method uses the smooth function to
approximate the normal map reformulation of nonlinear complementarity
problems. The algorithm is implemented and tested with two different plussmoothing
functions namely interior point plus-smooth function and piecewise
quadratic plus-smoothing function. These two functions are compared. Testing
of the algorithm is made with several known problems.Erkan, AliM.S
Algorithms for computing normally hyperbolic invariant manifolds
An effcient algorithm is developed for the numerical computation of normally hyperbolic invariant manifolds, based on the graph transform and Newton's method. It fits in the perturbation theory of discrete dynamical systems and therefore allows application to the setting of continuation. A convergence proof is included. The scope of application is not restricted to hyperbolic attractors, but extends to normally hyperbolic manifolds of saddle type. It also computes stable and unstable manifolds. The method is robust and needs only little specification of the dynamics, which makes it applicable to e.g. Poincaré maps. Its performance is illustrated on examples in 2D and 3D, where a numerical discussion is included.
Pruning, Pushdown Exception-Flow Analysis
Statically reasoning in the presence of exceptions and about the effects of
exceptions is challenging: exception-flows are mutually determined by
traditional control-flow and points-to analyses. We tackle the challenge of
analyzing exception-flows from two angles. First, from the angle of pruning
control-flows (both normal and exceptional), we derive a pushdown framework for
an object-oriented language with full-featured exceptions. Unlike traditional
analyses, it allows precise matching of throwers to catchers. Second, from the
angle of pruning points-to information, we generalize abstract garbage
collection to object-oriented programs and enhance it with liveness analysis.
We then seamlessly weave the techniques into enhanced reachability computation,
yielding highly precise exception-flow analysis, without becoming intractable,
even for large applications. We evaluate our pruned, pushdown exception-flow
analysis, comparing it with an established analysis on large scale standard
Java benchmarks. The results show that our analysis significantly improves
analysis precision over traditional analysis within a reasonable analysis time.Comment: 14th IEEE International Working Conference on Source Code Analysis
and Manipulatio
Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras
We consider the problem of finding the isolated common roots of a set of
polynomial functions defining a zero-dimensional ideal I in a ring R of
polynomials over C. We propose a general algebraic framework to find the
solutions and to compute the structure of the quotient ring R/I from the null
space of a Macaulay-type matrix. The affine dense, affine sparse, homogeneous
and multi-homogeneous cases are treated. In the presented framework, the
concept of a border basis is generalized by relaxing the conditions on the set
of basis elements. This allows for algorithms to adapt the choice of basis in
order to enhance the numerical stability. We present such an algorithm and show
numerical results
Explicit Mapping of Acoustic Regimes For Wind Instruments
This paper proposes a methodology to map the various acoustic regimes of wind
instruments. The maps can be generated in a multi-dimensional space consisting
of design, control parameters, and initial conditions. The bound- aries of the
maps are obtained explicitly in terms of the parameters using a support vector
machine (SVM) classifier as well as a dedicated adaptive sam- pling scheme. The
approach is demonstrated on a simplified clarinet model for which several maps
are generated based on different criteria. Examples of computation of the
probability of occurrence of a specific acoustic regime are also provided. In
addition, the approach is demonstrated on a design optimization example for
optimal intonation
Numerical periodic normalization for codim 2 bifurcations of limit cycles : computational formulas, numerical implementation, and examples
Explicit computational formulas for the coefficients of the periodic normal forms for codimension 2 (codim 2) bifurcations of limit cycles in generic autonomous ODEs are derived. All cases (except the weak resonances) with no more than three Floquet multipliers on the unit circle are covered. The resulting formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems on the interval [0, T], where T is the period of the critical cycle, as well as multilinear functions from the Taylor expansion of the ODE right-hand side near the cycle. The formulas allow one to distinguish between various bifurcation scenarios near codim 2 bifurcations of limit cycles. Our formulation makes it possible to use robust numerical boundary-value algorithms based on orthogonal collocation, rather than shooting techniques, which greatly expands its applicability. The implementation is described in detail with numerical examples, where numerous codim 2 bifurcations of limit cycles are analyzed for the first time
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