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Articles 1 - 2 of 2
Full-Text Articles in Algebra
Properties Of K-Isotropic Functions, Tianpei Jiang
Properties Of K-Isotropic Functions, Tianpei Jiang
Electronic Thesis and Dissertation Repository
The focus of this work is a family of maps from the space of $n \times n$ symmetric matrices, $S^n$, into the space $S^{{n \choose k}}$ for any $k=1,\ldots, n$, invariant under the conjugate action of the orthogonal group $O^n$. This family, called generated $k$-isotropic functions, generalizes known types of maps with similar invariance property, such as the spectral, primary matrix, isotropic functions, multiplicative compound, and additive compound matrices on $S^n$. The notion of operator monotonicity dates back to a work by L\"owner in 1934. A map $F :S^n \to S^m$ is called {\it operator monotone}, if $A \succeq B …
Metafork: A Compilation Framework For Concurrency Models Targeting Hardware Accelerators, Xiaohui Chen
Metafork: A Compilation Framework For Concurrency Models Targeting Hardware Accelerators, Xiaohui Chen
Electronic Thesis and Dissertation Repository
Parallel programming is gaining ground in various domains due to the tremendous computational power that it brings; however, it also requires a substantial code crafting effort to achieve performance improvement. Unfortunately, in most cases, performance tuning has to be accomplished manually by programmers. We argue that automated tuning is necessary due to the combination of the following factors. First, code optimization is machine-dependent. That is, optimization preferred on one machine may be not suitable for another machine. Second, as the possible optimization search space increases, manually finding an optimized configuration is hard. Therefore, developing new compiler techniques for optimizing applications …