195
195

Jun 19, 2010
06/10

by
Moore, J. W

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Approximation and matrix iteration techniques for solving automatic control equations

Topics: APPROXIMATION, AUTOMATIC CONTROL, EIGENVALUES, ITERATION, ITERATIVE SOLUTION, MATRICES...

202
202

Jul 23, 2010
07/10

by
NON

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No Abstract Available

Topics: FAILURE ANALYSIS, PROJECT MANAGEMENT, RISK, ITERATIVE SOLUTION, SYSTEMS ANALYSIS

200
200

Jul 26, 2010
07/10

by
Perry, Eileen M

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No Abstract Available

Topics: ALGORITHMS, CONJUGATE GRADIENT METHOD, CONVERGENCE, ITERATIVE SOLUTION, VARIANCE, ACCURACY,...

217
217

Jun 12, 2011
06/11

by
Kharchenko, Vasil

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We have carried out investigation of the EUV and X-ray emission spectra induced in interaction between the Solar Wind (SW) and interstellar neutral gas. The spectra of most important SW ions have been computed for the charge-exchange mechanism of X-ray emission using new accurate spectroscopic data from recent laboratory measurements and theoretical calculations. Total spectra have been constructed as a sum of spectra induced in the charge-exchange collisions by individual O(exp q), C(exp q),...

Topics: COMPUTATIONAL FLUID DYNAMICS, AERODYNAMICS, SENSITIVITY, ITERATIVE SOLUTION, DERIVATION, DESIGN...

243
243

Jul 6, 2010
07/10

by
LIEBERT, F

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IT WAS DERIVED FROM THERMO-CHEMICAL DATA THAT PHOSPHATE REDUCTION THROUGH MANNITE CAN NEVER PROVIDE THE BACTERIA WITH A GAIN IN ENERGY AND IT WAS FURTHER PROVEN THAT THIS PROCESS, WHEN IT TAKES PLACE, DOES NOT PROCEED ANALOG TO THE PROCESS OF DENITRIFICATION. IT WAS ALSO SHOWN, THAT THE RESULTS OF RUDAKOV'S ANALYSES DO NOT BY THEMSELVES CONSTITUTE PROOF OF A PHOSPHATE REDUCTION. BY MEANS OF SEVERAL DISTINCT QUALITATIVE REACTIONS REDUCTION PRODUCTS OF THE PHOSPHOROUS ACID WERE SEARCHED FOR BUT...

Topics: BALLOON FLIGHT, EARTH ROTATION, POSITION ERRORS, SATELLITE OBSERVATION, ITERATIVE SOLUTION,...

787
787

Jul 11, 2010
07/10

by
NON

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The problem and solution to the physical ozone irritation caused by ozone concentrations in the cabin of high-altitude aircraft are presented.

Topics: NUMERICAL ANALYSIS, REAL VARIABLES, TRANSCENDENTAL FUNCTIONS, ALGORITHMS, DIFFERENTIAL EQUATIONS,...

369
369

Jul 6, 2010
07/10

by
SANTACESARIA, E.; GIUFFRE, L

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A GAS CHROMATOGRAPHY METHOD IS PROPOSED FOR PERFORMING A QUANTITATIVE ASSAY OF HYDRAZINE AND ITS USUAL SPLITTING PRODUCTS, N2, NH3 AND H2. THE METHOD IS BASED ON THE USE OF TWO SWITCHABLE GAS CHROMATOGRAPHY COLUMNS; WATER AND HYDRAZINE ARE ASSAYED ON ONE NITROGEN AND AMONIA ON THE OTHER. SINCE HYDROGEN IS GENERATED BY THE SPLITTING OF HYDRAZINE, IT IS ASSAYED BY A DIFFERENTIAL CALCULATION FROM THE KNOWN CONVERSION PATTERNS OF HYDRAZINE, AFTER HAVING SETTLED THE MATTER OF THE NITROGEN BALANCE....

Topics: BALLOONS, DOPPLER EFFECT, EARTH ROTATION, POSITION ERRORS, SATELLITE OBSERVATION, ITERATIVE...

171
171

Jul 12, 2010
07/10

by
Winn, C. B.; Huston, W

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A geostationary reference satellite (REFSAT) that broadcasts every four seconds updated GPS satellite coordinates was developed. This procedure reduces the complexity of the GPS receiver. The economic and performance payoffs associated with replacing maritime stripborne navigation systems with NAVSTAR was quantified and the use of NAVSTAR for measurements of ocean currents in the broad ocean areas of the world was evaluated.

Topics: CRITERIA, INFORMATION SYSTEMS, MANAGEMENT PLANNING, SYSTEMS ANALYSIS, EDUCATION, HUMAN FACTORS...

563
563

Jun 27, 2010
06/10

by
Hersh, A. S.; Hayden, R. E

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Aerodynamic sound radiation from lifting surfaces in smooth and turbulent flow

Topics: DIFFERENCE EQUATIONS, ELECTRODYNAMICS, OPERATORS (MATHEMATICS), APPROXIMATION, GAS DYNAMICS,...

An algorithm is developed to find a quick way to determine the origin O in the complex plane C within the image of Q (a subset of the parameter space R(sup n)) under the multilinear function p(j omega, q) = f(q) + g(q)j for a fixed omega.

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, ITERATIVE SOLUTION, LINEAR TRANSFORMATIONS,...

The major difficulties in determination of the steady-state properties of a Markovian queuing network by numerical solution of a set of linear balance equations are the choice of vector representation of the states, the generation and storage of the states, and generation, storage and solution of the balance equations. Lexicographic sequencing of the vector representations are shown in this thesis to lead to efficiencies in the storage and solution of the balance equations and to provide a key...

Topics: queues, queuing models, models for computers, networks of queues, iterative solution methods,...

215
215

Jul 5, 2010
07/10

by
Hohenemser, K. H.; Yin, S. K

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The effects of various gust alleviation methods on the random blade response in flapping were studied analytically, assuming a rigid rotor support. The analytical model assumes rigid flapping blades with elastic root restraints. Linearized equations which are approximately valid at low lift conditions were used. Because of the interblade coupling from the feedback devices, the method of multiblade generalized coordinates was most convenient and was extended to include coning, differential...

Topics: CYLINDRICAL BODIES, ELASTOHYDRODYNAMICS, LUBRICANTS, COMPRESSIBILITY, DEFORMATION, FILM THICKNESS,...

509
509

Jul 6, 2010
07/10

by
Kelly, J. B.; June, R. R

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Methods to eliminate or reduce residual stresses in aircraft metal structures reinforced by filamentary composites are discussed. Residual stress level reductions were achieved by modifying the manufacturing procedures used during adhesive bonding. The residual stress alleviation techniques involved various forms of mechanical constraint which were applied to the components during bonding. Nine methods were evaluated, covering a wide range in complexity. All methods investigated during the...

Topics: DESCENT TRAJECTORIES, ITERATIVE SOLUTION, TRAJECTORY OPTIMIZATION, ALGORITHMS, BOUNDARY VALUE...

801
801

Jul 26, 2010
07/10

by
Allen, James G.; Sikora, Scott E

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The objective of this effort was to develop a Knowledge Capture System (KCS) for the Integrated Test Facility (ITF) at the Dryden Flight Research Facility (DFRF). The DFRF is a NASA Ames Research Center (ARC) facility. This system was used to capture the design and implementation information for NASA's high angle-of-attack research vehicle (HARV), a modified F/A-18A. In particular, the KCS was used to capture specific characteristics of the design of the HARV fly-by-wire (FBW) flight control...

Topics: ERROR ANALYSIS, FINITE ELEMENT METHOD, ITERATIVE SOLUTION, NONLINEAR SYSTEMS, SHELL THEORY,...

269
269

Jun 21, 2010
06/10

by
Mayo, J. W.; Michael, J. E

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Distribution of currents to circuits using electrical adaptor

Topics: APPROXIMATION, ITERATIVE SOLUTION, NONLINEAR EQUATIONS, ALGORITHMS, BANACH SPACE, BOUNDARY VALUE...

247
247

May 21, 2011
05/11

by
Harrington, Richard F

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The feasibility of detecting the cold core of the wake vortex from the wingtips of an aircraft using a passive microwave radiometer was investigated. It was determined that there is a possibility that a cold core whose physical temperature drop is 10 C or greater and which has a diameter of 5 m or greater can be detected by a microwave radiometer. The radiometer would be a noise injection balanced Dicke radiometer operating at a center frequency of 60 GHz. It would require a noise figure of 5...

Topics: CONJUGATE GRADIENT METHOD, INTEGRATED CIRCUITS, LAYOUTS, MULTIGRID METHODS, ALGEBRA, ALGORITHMS,...

NASA regulations specify that formal risk analysis be performed on a program at each of several milestones. Program risk analysis is discussed as a systems analysis approach, an iterative process (identification, assessment, management), and a collection of techniques. These techniques, which range from extremely simple to complex network-based simulation, are described in this handbook in order to provide both analyst and manager with a guide for selection of the most appropriate technique....

Topics: NASA Technical Reports Server (NTRS), FAILURE ANALYSIS, PROJECT MANAGEMENT, RISK, ITERATIVE...

264
264

Jul 21, 2010
07/10

by
Rose, W. C

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The angle of attack (AOA) tandem cavity wind tunnel experiment was prepared. Actual wind tunnel testing started shortly after the beginning of 1985. A multi-probe aerodynamic rake was designed and installed for use in surveying the shear layers present over the open cavity on the Kuiper Airborne Observatory (KAO). The nature of the behavior of the thermal environment within the KAO cavity at operational altitudes was determined. Assistance was given in the design of the cavity for the...

Topics: ALGORITHMS, ELLIPTIC DIFFERENTIAL EQUATIONS, ELLIPTIC FUNCTIONS, ITERATIVE SOLUTION, PARTIAL...

191
191

May 31, 2011
05/11

by
Rosendahl, Uwe; Dreyer, Michael E.; Rath, Hans J.; Motil, Bria

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We investigate forced liquid flows through open capillary channels with free surfaces experimentally. The experiments were performed under low gravity conditions in the Bremen Drop Tower and on board the sounding rocket TEXUS-37. Open capillary channels (vanes) are used in surface tension tanks to transport the propellant and to provide a flow path for the bubble-free liquid supply to the thrusters. Since the free surfaces can only withstand a certain pressure differential between the liquid...

Topics: OPTIMIZATION, LARGE SCALE INTEGRATION, ENGINEERING, SYSTEMS SIMULATION, FINITE ELEMENT METHOD,...

1,023
1.0K

Jun 21, 2010
06/10

by
Jensen, A.; Lehman, W

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Glider flight path at takeoff using tow winch

Topics: NONEQUILIBRIUM FLOW, SLENDER BODIES, SUPERSONIC FLOW, TWO DIMENSIONAL BODIES, WAVE DRAG, CONTOURS,...

An algorithm is described which solves the parameters X = (x1,x2,...,xm) and p in an approximation problem Ax nearly equal to y(p), where the parameter p occurs nonlinearly in y. Instead of linearization methods, which require an approximate value of p to be supplied as a priori information, and which may lead to the finding of local minima, the proposed algorithm finds the global minimum by permitting the use of series expansions of arbitrary order, exploiting an a priori knowledge that the...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, FUNCTIONS (MATHEMATICS), ITERATIVE SOLUTION,...

588
588

Jul 26, 2010
07/10

by
Garrett, L. Bernard; Ferebee, Melvin J., Jr.; Queijo, Manuel J.; Butterfield, Ansel J

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A configuration for a second-generation advanced technology space station has been defined in a series of NASA-sponsored studies. Definitions of subsystems specifically addressed opportunities for beneficial synergistic interactions and those potential synergies and their benefits are identified. One of the more significant synergistic benefits involves the multi-function utilization of water within a large system that generates artificial gravity by rotation. In such a system, water not only...

Topics: COUPLING, GEOIDS, NONLINEARITY, OPTIMIZATION, PARAMETERIZATION, EARTH CORE, EARTH MANTLE,...

A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory...

Topics: NASA Technical Reports Server (NTRS), AUTOMATIC PILOTS, LAUNCH VEHICLES, LINEAR PROGRAMMING,...

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the...

Topics: NASA Technical Reports Server (NTRS), CONSTRAINTS, ITERATION, OPTIMIZATION, PARTIAL DIFFERENTIAL...

Wozencraft and Kennedy have suggested that the appropriate demodulator criterion of goodness is the cut-off rate of the discrete memoryless channel created by the modulation system; the criterion of goodness adopted in this note is the symmetric cut-off rate which differs from the former criterion only in that the signals are assumed equally likely. Massey's necessary condition for optimal demodulation of binary signals is generalized to M-ary signals. It is shown that the optimal demodulator...

Topics: NASA Technical Reports Server (NTRS), DECISION THEORY, DEMODULATION, SIGNAL ANALYSIS, ASYMPTOTES,...

Recent work on the mathematical foundations of optimization has begun to uncover its rich structure. In particular, the "No Free Lunch" (NFL) theorems state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance. In this paper we present a general framework covering more search scenarios. In addition to the optimization scenarios...

Topics: NASA Technical Reports Server (NTRS), THEOREMS, ALGORITHMS, OPTIMIZATION, HEURISTIC METHODS,...

We present an iterative technique in which model checking and static analysis are combined to verify large software systems. The role of the static analysis is to compute partial order information which the model checker uses to reduce the state space. During exploration, the model checker also computes aliasing information that it gives to the static analyzer which can then refine its analysis. The result of this refined analysis is then fed back to the model checker which updates its partial...

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, SOFTWARE ENGINEERING, STATIC MODELS,...

We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, ITERATIVE SOLUTION, MARKOV CHAINS, RELAXATION...

598
598

Jul 23, 2010
07/10

by
Strganac, Thomas W

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A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a...

Topics: COMPRESSIBLE FLOW, COMPUTATIONAL FLUID DYNAMICS, DELTA WINGS, INTEGRAL EQUATIONS, VORTEX SHEETS,...

285
285

Jun 21, 2010
06/10

by
Nitsch, P.; Riester, E.; Schmidt, N

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Maximum speed wind tunnel for reentry measurements

Topics: CESIUM PLASMA, COLLISIONLESS PLASMAS, EMITTERS, ITERATIVE SOLUTION, PLASMA SHEATHS, HIGH...

A creeping-random-search algorithm is applied to different types of problems in the field of parameter identification. The studies are intended to demonstrate that a random-search algorithm can be applied successfully to these various problems, which often cannot be handled by conventional deterministic methods, and, also, to introduce methods that speed convergence to an extremal of the problem under investigation. Six two-parameter identification problems with analytic solutions are solved,...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, PARAMETERIZATION, RANDOM WALK, ITERATIVE...

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a...

Topics: NASA Technical Reports Server (NTRS), EIGENVALUES, LAPLACE TRANSFORMATION, SPHERES, ELLIPTIC...

The Iterative Transform Phase Diversity algorithm is designed to solve the problem of recovering the wavefront in the exit pupil of an optical system and the object being imaged. This algorithm builds upon the robust convergence capability of Variable Sampling Mapping (VSM), in combination with the known success of various deconvolution algorithms. VSM is an alternative method for enforcing the amplitude constraints of a Misell-Gerchberg-Saxton (MGS) algorithm. When provided the object and...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, IMAGE ANALYSIS, WAVE FRONTS, IMAGE PROCESSING,...

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is,...

Topics: NASA Technical Reports Server (NTRS), DIGITAL COMPUTERS, ITERATIVE SOLUTION, POLYNOMIALS,...

232
232

Aug 2, 2010
08/10

by
Schmidt, E.; Grein, H.-D

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A method to solve the inverse problem of supercritical blade-to-blade flow on stream surfaces of revolution with variable radius and variable stream surface thickness in a relative system is described. Some aspects of shockless design and of leading edge resolution in the numerical procedure are depicted. Some supercritical compressor cascades were designed and their complete flow field results were compared with computations of two different analysis methods.

Topics: COMPUTER AIDED DESIGN, TURBOMACHINERY, CONFERENCES, DESIGN ANALYSIS, OPTIMIZATION, AERODYNAMICS,...

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, LINEAR EQUATIONS, MATRICES (MATHEMATICS),...

173
173

Jul 21, 2010
07/10

by
Draine, B. T

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Dust formation around cool giant and supergiant stars is examined in terms of grain formulation. Optical properties of small clusters, molecular physics of cluster nucleation and growth, circumstellar mass flows, and their application to alpha Ori are discussed.

Topics: COMPUTERIZED SIMULATION, LIQUID OXYGEN, SPACE SHUTTLE MAIN ENGINE, TURBINE PUMPS, COOLANTS, GRAPHS...

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector...

Topics: NASA Technical Reports Server (NTRS), FEEDBACK, ITERATIVE SOLUTION, LINEAR SYSTEMS, OPTIMAL...

A Computer Aided Design (CAD) system is presented which supports the iterative process of design, the dimensional continuity between mating parts, and the hierarchical structure of the parts in their assembled configuration. Prolog, an interactive logic programming language, is used to represent and interpret the data base. The solid geometry representing the parts is defined in parameterized form using the swept volume method. The system is demonstrated with a design of a spring piston.

Topics: NASA Technical Reports Server (NTRS), COMPUTER AIDED DESIGN, LOGIC PROGRAMMING, GEOMETRY,...

4
4.0

Oct 8, 2020
10/20

by
Patterson, Walter Mead

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183 pages ; 25 cm

Topics: Operator equations, Iterative methods (Mathematics), Hilbert space, Équations à opérateurs,...

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial...

Topics: NASA Technical Reports Server (NTRS), ALGEBRA, ITERATIVE SOLUTION, LINEAR EQUATIONS, ALGORITHMS,...

Interferometric tomography in the presence of an opaque object is investigated. The developed iterative algorithm does not need to augment the missing information. It is based on the successive reconstruction of the difference field, the difference between the object field to be reconstructed and its estimate, only in the difined region. The application of the algorithm results in stable convergence.

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, DIFFERENCE EQUATIONS, INTERFEROMETRY, TOMOGRAPHY,...

197
197

Jun 15, 2011
06/11

by
Perrill, W. A

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The structure and use of an Interactive Graphics Packaging Program (IGPP), conceived to apply computer graphics to the design of packaging electronic circuits onto printed circuit boards (PCB), were described. The intent was to combine the data storage and manipulative power of the computer with the imaginative, intuitive power of a human designer. The hardware includes a CDC 6400 computer and two CDC 777 terminals with CRT screens, light pens, and keyboards. The program is written in FORTRAN 4...

Topics: AIRCRAFT DESIGN, TIME SHARING, WINGS, AIRCRAFT STRUCTURES, COMPUTER GRAPHICS, INTERACTIONS, MAN...

Techniques for solving the feature selection problem are presented. Topics discussed include the reduction of the number of variables in "best b", and the iterative selection of H sub i.

Topics: NASA Technical Reports Server (NTRS), MATRICES (MATHEMATICS), PROBLEM SOLVING, ITERATIVE SOLUTION,...

Constrained Chebyshev approximation problems of the type with minimum (p is an element of Pi(sub n):p(c)=1) and maximum (z is an element of E) with /p(z)/ are considered. Here Pi(sub n) denotes the set of all complex polynomials of degree at most n, E is any ellipse in the complex plane, and c is an element of C/E. Such approximation problems arise in the context of optimizing semi-iterative methods for the solution of large, sparse systems of linear equations Ax=b with complex non-Hermitian...

Topics: NASA Technical Reports Server (NTRS), CHEBYSHEV APPROXIMATION, ITERATIVE SOLUTION, LINEAR...

232
232

Jun 27, 2010
06/10

by
Turk, R. R

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Production method for manufacturing porous tungsten bodies from tungsten powder particles

Topics: DYNAMIC STRUCTURAL ANALYSIS, ITERATIVE SOLUTION, MODAL RESPONSE, RAYLEIGH-RITZ METHOD, STATIC...

The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized...

Topics: NASA Technical Reports Server (NTRS), DISTRIBUTION FUNCTIONS, ITERATIVE SOLUTION, PROBABILITY...

During this contract period, our work has focused on improvements to elliptic grid generation methods. There are two principle objectives in this project. One objective is to make the elliptic methods more reliable and efficient, and the other is to construct a modular code that can be incorporated into the National Grid Project (NGP), or any other grid generation code. Progress has been made in meeting both of these objectives. The two objectives are actually complementary. As the code...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL GRIDS, ELLIPTIC DIFFERENTIAL EQUATIONS, GRID...

The real zeros of the transcendental function y = ax + becx are characterized, and the results should alleviate the difficulty of determining their existence, location, and number.

Topics: NASA Technical Reports Server (NTRS), NUMERICAL ANALYSIS, REAL VARIABLES, TRANSCENDENTAL FUNCTIONS,...

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems...

Topics: NASA Technical Reports Server (NTRS), CHEBYSHEV APPROXIMATION, ITERATIVE SOLUTION, PRECONDITIONING,...