Preconditioning with Matrix Factorization
نویسندگان
چکیده
Pietsch Factorization and Grothendieck Factorization are the two landmark theorems in modern functional analysis. They were first introduced to the numerical linear algebra community by the work of Joel A. Tropp in the column subset selection problem, which seeks to extract from a matrix a column submatrix that has lower spectral norm. Despite their broad application in functional analysis, the application of both factorization techniques are still not well studied in numerical linear algebra literatures. In this project, we propose that Pietsch factorization and Grothendieck factorization can be used to find the preconditioner of the matrix. The performance is compared with standard precondition techniques by preconditioning the conjugate gradient method.
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