Spelling suggestions: "subject:"[een] NEWTON RAPHSON METHOD"" "subject:"[enn] NEWTON RAPHSON METHOD""
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The dynamics of Newton's method on cubic polynomialsMiller, Shannon N. January 2006 (has links)
Theses (M.A.)--Marshall University, 2006. / Title from document title page. Includes abstract. Document formatted into pages: contains v, 53 pages. Bibliography: p. 52-53.
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Studies of Extensions of HRM-SDT for Constructed ResponsesZhou, Xiaoliang January 2019 (has links)
This research examines an ordered perception rater model, an extension of the equal perception signal detection theory (SDT) latent class rater model. The expectation-maximization algorithm and the Newton-Raphson algorithm are used to estimate parameters. Four simulation studies are conducted to answer three research questions.
Simulation studies 1 and 2 fit correct models to the data. Simulation study 1 generates one hundred data sets from the equal perception rater model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the equal perception model. Parameter recovery is excellent for fully-crossed design and reasonable for BIB design, and all rater effects are detected. Simulation study 2 generates one hundred simulated data sets from the ordered perception model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the ordered perception rater model. Although parameter recovery is biased for some parameters in the BIB design, all rater effects are recovered.
Simulation studies 3 and 4 fit wrong models to the data. Simulation study 3 fits equal perception models to the fully-crossed and BIB ordered perception data sets generated in simulation study 2. All rater effects are revealed, although rater effects are distorted to some extent in the BIB design. Simulation study 4 fits ordered perception models to the fully-crossed and BIB equal perception data sets generated in study 1. All rater effects are recovered.
Using essay scores from a large-scale language test, an empirical study is conducted. Both the equal and the ordered perception models are fitted. Information criteria favor the equal perception model.
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An Investigation of Rupture in Thin Fluid FilmsBaur, Robin 01 December 2005 (has links)
The behavior of a fluid with a thin capillary meniscus can be modelled on a one-dimensional domain Ω = [−L, L] by the thin film equation ht = −(hnhxxx)x with boundary conditions hx(±L) = ±α (giving a fixed contact angle) and hxxx(±L) = 0 (prohibiting mass flux). It is desirable to know whether or not such a film experiences rupture; that is, whether there exists some x0, t0 (with t0 possibly ∞) such that h(x0, t0) = 0, corresponding to the appearance of a dry spot. We approach this problem using energy methods, which use the conservation or dissipation of quantities such as mass, surface area, coating energy, and other more abstract quantities to describe the behavior of the fluid. We present a brief analysis of the behavior of some of these energies, as well as a proof that, given certain assumptions, rupture cannot occur in a thin capillary meniscus for n > 4 and, in more restricted cases, for n > 7/2. We also show that rupture must occur for 0 < n < 1/2. We describe the asymptotic behavior of the regions in which rupture occurs. We also describe the numerical implementation of this problem and the advantages and drawbacks of using certain prewritten solvers in MATLAB and new implementations of θ-weighted schemes and the Newton-Raphson method. We propose uses of these numerical methods to make further progress on the problem.
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Nonlinear solvers for a model problem of fluid flow in the subsurface /Biederman, Shannon Miriah. January 1900 (has links)
Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaf 53). Also available on the World Wide Web.
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Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's methodChoi, Yan-yu., 蔡欣榆. January 2006 (has links)
published_or_final_version / abstract / Mathematics / Master / Master of Philosophy
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Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-spaceUnknown Date (has links)
One of the most fundamental problems in classical general relativity is the
measure of e↵ective mass of a pure gravitational field. The principle of equivalence
prohibits a purely local measure of this mass. This thesis critically examines the most
recent quasi-local measure by Wang and Yau for a maximally rotating black hole
spacetime. In particular, it examines a family of spacelike 2-surfaces with constant
radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the
Wang and Yau quasi-local energy has yet to be explored. In this region, the results of
this thesis indicate that the Wang and Yau quasi-local energy yields complex values
and is essentially equivalent to the previously defined Brown and York quasi-local
energy. However, an application of their quasi-local mass is suggested in a dynamical
setting, which can potentially give new and meaningful measures. In supporting this
thesis, the development of a novel adiabatic isometric mapping algorithm is included.
Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical
topology into Euclidean 3-space necessary for completing the calculation of quasilocal
energy in numerical relativity codes. The innovation of this algorithm is the
guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm
to provide accuracy of the edge lengths up to a user set tolerance. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection
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Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's methodChoi, Yan-yu. January 2006 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.
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Rigorous and reasonable error bounds for the numerical solution of dynamical systemsKuhn, Wolfgang 12 1900 (has links)
No description available.
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Guaranteed error bounds for computed solutions of nonlinear two-point boundary value problemsTalbot, Thomas D. January 1968 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. Description based on print version record. Includes bibliographical references (p. 185-187).
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CONVERSION FROM ENGINEERING UNITS TO TELEMETRY COUNTS ON DRYDEN FLIGHT SIMULATORSFantini, Jay A. 10 1900 (has links)
International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / Dryden real-time flight simulators encompass the simulation of pulse code modulation (PCM) telemetry signals. This paper presents a new method whereby the calibration polynomial (from first to sixth order), representing the conversion from counts to engineering units (EU), is numerically inverted in real time. The result is less than onecount error for valid EU inputs. The Newton-Raphson method is used to numerically invert the polynomial. A reverse linear interpolation between the EU limits is used to obtain an initial value for the desired telemetry count. The method presented here is not new. What is new is how classical numerical techniques are optimized to take advantage of modern computer power to perform the desired calculations in real time. This technique makes the method simple to understand and implement. There are no interpolation tables to store in memory as in traditional methods. The NASA F-15 simulation converts and transmits over 1000 parameters at 80 times/sec. This paper presents algorithm development, FORTRAN code, and performance results.
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