%A George Ostrouchov
%T ANOVA Model Fitting via Sparse Matrix Computations
%R ORNL Technical Report
%I Oak Ridge National Laboratory
%D August 1985
%X The least-squares computational approach is used in fitting
analysis of variance models when data are unbalanced or incomplete.
For large models containing factors with many levels, standard
statistical packages require enormous amounts of time and storage due
to the size of the crossproducts matrix.  The model matrix X (often
called the design matrix) consists of dummy variables and is sparse,
thus great reduction in time and storage can be achieved by viewing
this as a sparse matrix problem.
  A method, based on orthogonal Givens factorization of a maximal
rank set of sparse columns of X, for computing estimates and residual
sums of squares is presented.  Selection of a maximal rank set of
sparse columns is a key part of this method and is based on the linear
dependencies between columns of the model matrix.  The linear
dependencies are described using a notation based on index sets
associated with model terms.
  Time and storage requirements of the new algorithm are compared to
the requirements of GLIM, which uses the same basic numerical algorithm
that is used in most statistical packages.  Both requirements of the
new algorithm are less by up to three orders of magnitude for large
models and are competitive for small models.

%A V. Alexiades
%A J.B. Drake
%A G.A. Geist
%A G.E. Giles
%A A.D. Solomon
%A R.F. Wood
%T Mathematical Modeling of Laser-Induced Ultrarapid Melting and Solidification
%R Technical Report ORNL-6129
%I Oak Ridge National Laboratory
%D July 1985
%X Mathematical and numerical aspects of laser induced phase change
modeling are dicussed.  Several numerical formulations, including
explicit and implicit enthalpy, adaptive grid finite volume and
front tracking are derived and results are presented.  In addition,
a novel hyperbolic formulation is explored analytically and
numerically.  The explicit enthalpy approach allows the greatest
flexibility and efficiency in modeling problems with complicated
phase transitions.

%A Max Morris
%A Vasili Alexiades
%T Sensitivity Analysis of a Numerically Simulated
HgCdTe Solidification Process by Statistical Methods
%R Technical Report ORNL-6210
%I Oak Ridge National Laboratory
%D August 1985
%X Statistical response surface methodology is applied to the problem of
determining simple approximations for outputs as functions of input
parameter values in a numerical simulation of the solidification of
a mercury-cadmium-telluride alloy.  The approximating polynomials are
then differentiated with respect to parameter values to determine
sensitivities.  A table of percent changes in output values as a
result of one per cent changes in parameter values is presented.
The empirical procedure used constitutes an unorthodox application
of the statistical methodology, but it is easy to use, quite generally
applicable and very effective.

%A Vasili Alexiades
%A George A. Geist
%A A. D. Solomon
%T Numerical Simulation of a HgCdTe Solidification Process
%R Technical Report ORNL-6127
%I Oak Ridge National Laboratory
%D August 1985
%X The solidification of a cylindrical ingot of mercury-cadmium-telluride is
modeled taking into account both heat conduction and solute diffusion.
Values of the relevant thermophysical parameters of the pseudo-binary
HgTe-CdTe are compiled.  The model is implemented numerically by a
finite-difference discretization and results of the simulation of a
freezing experiment are reported.

%A George A. Geist
%A Michael T. Heath
%T Parallel Cholesky Factorization on a Hypercube Multiprocessor
%R Technical Report ORNL-6190
%I Oak Ridge National Laboratory
%D July 1985
%X Two types of message-passing parallel algorithms are developed for
solving symmetric systems of linear equations on a hypercube
multiprocessor.  One type involves broadcast communication among
processors, and the other involves communication along a ring of
processors.  Details are provided in the form of C programs that
implement the algorithms on a hypercube simulator and which should run
with little modification on real hypercube hardware.  Performance of
the various algorithms is demonstrated by means of processor
utilization graphs and parallel speedup curves.

%A Michael T. Heath
%T Parallel Cholesky Factorization in
Message-Passing Multiprocessor Environments
%R Technical Report ORNL-6150
%I Oak Ridge National Laboratory
%D May 1985
%X Parallel algorithms are presented for computing the Cholesky
factorization on multiprocessors having only private local memory.
Synchronization of multiple processes is based on message passing.
Several possible processor interconnection networks are considered.

%A George A. Geist
%T Efficient Parallel LU Factorization with Pivoting
on a Hypercube Multiprocessor
%R Technical Report ORNL-6211
%I Oak Ridge National Laboratory
%D August 1985
%X A message-passing parallel algorithm is developed for forming
the LU factors of general non-singular matrices on a hypercube
multiprocessor.  Partial pivoting is performed to ensure numerical
stability, but the scheduling of tasks is such that the pivot search
in the parallel algorithm is completely masked.  Empirical tests show
that the load imbalance produced by random pivoting causes a 5%-14%
increase in execution time.  A complementary parallel triangular
solution algorithm is also given.  Comparisons with the non-pivoting
case are used to demonstrate the efficiency of this new algorithm.