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At least 19 records

On the variational equations for Householder transformations in feature selection

Results that suggest the possibility of using a sequential monotone process for solving the feature selection problem using Householder transformations are applied to the divergence separability criterion and an expression for the gradient of the divergence with respect to the generator of a single Householder transformation will be developed. This expression for the gradient is used in any number of differential correction schemes (iterators) that attempt to extremize the divergence. Data sets provided by the Earth Observations Division-JSC are used to demonstrate selecting the Householder transformations that generate the kxn matrix defining the best (in the sense of extremizing the divergence) k linear combinations of features. The tests allow initial comparisons to be made with results. In particular, this technique does not appear to require initial guesses for the iterator to be generated without replacement, exhaustive search, or other similar schemes.

Decell, H. P., Jr.

An inquiry into the household economy

The value of the time which people devote to each activity of their lives is compared with the money they spend on the activity. After tax wage rates are used to value an individual's time. The enormous size of the household economy and the fact that for most activities the value of the consumer's time devoted to an activity exceeds the money expenditures on the activity, suggest that there are many opportunities for productivity improvements in the household economy which have been overlooked in most traditional thinking on productivity.

Samuelson, R. D.

A parallel Householder tridiagonalization stratagem using scattered square decomposition

The parallel stratagem in this paper uses scattered square decomposition, introduced by Fox (1985), for its data assignment and then exploits parallelism in the solution steps of the sequential Householder tridiagonalization algorithm. One may condense a real symmetric full matrix A of order n into a tridiagonal form by the stratagem in concurrent machines where N(=D-squared) processors are used. Expressions for efficiency and speedup are given for the evaluation of the stratagem. An alternative stratagem which requires less data transmission but more computations is also discussed. The results shown that the Householder method of tridiagonalization may be implemented on a concurrent machine efficiently by scattered square decomposition provided that the number of matrix elements contained in each processor is much larger than the number of processors of the concurrent machine, and the ratio of the time to transmit one data item from one processor to any other processor to the time to perform a floating-point arithmetic operation is small enough.

Chang, H. Y.

A Storage-Efficient WY Representation for Products of Householder Transformations

A product Q=P1 ... P(sub r) of m x m Householder matrices can be written in the form Q = I + WY(sup T), where W and Y are each m x r. This is called the WY representation of Q. It is of interest when implementing Householder techniques in high-performance computing environments that are especially good at matrix-matrix multiplication. In this note a storage-efficient way to implement the WY representation is described. In particular, it is shown how the matrix Q can be expressed in the form Q = I + YTY(sup T). Usually r much less than m and so this 'compact' WY representation requires less storage. When compared with the recent block-reflector strategy the new technique still has a storage advantage and involves a comparable amount of work.

Schreiber, Robert

Development of a household waste treatment subsystem, volume 1

The domestic waste treatment subsystem was developed to process the daily liquid and non-metallic solid wastes provided by a family of four people. The subsystem was designed to be connected to the sewer line of a household which contained water conservation features. The system consisted of an evaporation technique to separate liquids from solids, an incineration technique for solids reduction, and a catalytic oxidizer for eliminating noxious gases from evaporation and incineration processes. All wastes were passed through a grinder which masticated the solids and deposited them in a settling tank. The liquids were transferred through a cleanable filter into a holding tank. From here the liquids were sprayed into an evaporator and a spray chamber where evaporation occurred. The resulting vapors were processed by catalytic oxidation. Water and latent energy were recovered in a combination evaporator/condenser heat exchanger. The solids were conveyed into an incinerator and reduced to ash while the incineration gases were passed through the catalytic oxidizer along with the processed water vapor.

Gresko, T. M.

Error analysis of householder transformations as applied to the standard and generalized eigenvalue problems

Backward error analyses of the application of Householder transformations to both the standard and the generalized eigenvalue problems are presented. The analysis for the standard eigenvalue problem determines the error from the application of an exact similarity transformation, and the analysis for the generalized eigenvalue problem determines the error from the application of an exact equivalence transformation. Bounds for the norms of the resulting perturbation matrices are presented and compared with existing bounds when known.

Ward, R. C.

The potential of carbon fiber induced shock hazards in household toasters

The average exposure to carbon fibers which produced a short and potential shock hazard in a household toaster was determined. Toasters are normally in the off state. They are used for brief periods during the day and have timed cycles during which power is applied. The possibility of a short occurring from the heating element to the case was investigated to find the exposure levels at which a potential shock hazard could appear. The short produced was tested to determine its importance.

Meyers, J. A.

A parallel householder tridiagonalization stratagem using scattered row decomposition

Householder's method for tridiagonalizing a real symmetric matrix, a major step in evaluating eigenvalues of the matrix, is modified into a parallel algorithm for a concurrent machine of message passing type. Each processor of the concurrent machine has its own CPU, communications control and local memory. Messages are passed through connections between processors. Although the basic algorithm is inherently serial, the computations can be spread over all processors by scattering different rows of the matrix into processors, hence the term 'Scattered Row Decomposition'. The steps in the serial and the parallel algorithms are identified. Expressions for efficiency and speedup are given in terms of problem and machine parameters. For a concurrent machine of ring type interconnection, a selected representative problem of large order exhibits efficiency approaching 66 per cent.

Chang, H. Y.

Experiments in materials science from household items

Everyday household items are used to demonstrate some unique properties of materials. A coat hanger, rubber band, balloon, and corn starch have typical properties which we often take for granted but can be truly amazing.

Spiegel, F. Xavier

The computation of generalized cross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models

An efficient algorithm for computing the generalized cross-validation function for the general cross-validated regularization/smoothing problem is provided. This algorithm is appropriate for problems where no natural structure is available, and the regularization/smoothing problem is solved (exactly) in a reproducing kernel Hilbert space. It is particularly appropriate for certain multivariate smoothing problems with irregularly spaced data, and certain remote sensing problems, such as those that occur in meteorology, where the sensors are arranged irregularly. The algorithm is applied to the fitting of interaction spline models with irregularly spaced data and two smoothing parameters; favorable timing results are presented. The algorithm may be extended to the computation of certain generalized maximum likelihood (GML) functions. Application of the GML algorithm to a problem in numerical weather forecasting, and to a broad class of hypothesis testing problems, is noted.

Gu, Chong

Water recovery and solid waste processing for aerospace and domestic applications. Volume 1: Final report

A comprehensive study of advanced water recovery and solid waste processing techniques employed in both aerospace and domestic or commercial applications is reported. A systems approach was used to synthesize a prototype system design of an advanced water treatment/waste processing system. Household water use characteristics were studied and modified through the use of low water use devices and a limited amount of water reuse. This modified household system was then used as a baseline system for development of several water treatment waste processing systems employing advanced techniques. A hybrid of these systems was next developed and a preliminary design was generated to define system and hardware functions.

Murray, R. W.

Quick, easy to prepare freeze-dried soups

Major advantages of soups are that they totally rehydrate in less than five minutes in water at approximately 150 deg F, maintain flavor and quality stability for two weeks in a 100 F environment, and remain stable for considerably longer at ambient temperatures. They are suitable for either household or field use.

Ramirez, R. V.

Buckling and vibration analysis for stiffened orthotropic shells of revolution.

Development of a numerical method, using the multistep integration approach, in which the buckling and vibration analyses are formulated as a succession of linear eigenvalue problems. The method does not require an estimate of the eigenvector, and once an eigenvalue has been converged good estimates for other eigenvalues are automatically available. This is accomplished through the use of an in-core Householder scheme for solution of the eigenvalue problem. Furthermore, since the method uses an eigenvalue solution, the possibility of missing modes is eliminated.

Svalbonas, V.