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{\large Qiqi Wang \\
{\bf A residual-based optimal interpolation scheme for model reduction}}

77 Massachusetts Ave \\ Bldg 33 Rm 408 \\ Cambridge \\ MA 02139
\\
{\tt qiqi@mit.edu}\\
Paul Constantine\end{center}

In this work we consider the problem of a matrix equation whose
matrix and right hand side depend on a set of parameters. We propose a
interpolation method that approximates the value of the output at given
parameter values by a linear combination of solutions already computed at
arbitrarily specified points in the parameter space. To compute the
interpolant, we solve an optimization problem that yields the
coefficients of the linear combination. The framework is very general and
begets a straightforward adaptive strategy for choosing new solutions to
add to the approximation based on the largest minimum value of the
objective function over the parameter space. Our interpolation based
model reduction approach also easily generalizes to nonlinear systems of
equations. The efficiency of our approach will be demonstrated with
numerical examples on both linear and nonlinear problems.


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