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In this letter, we introduce an efficient algorithm to estimate the noise correlation matrix in the initial stage of the hyperspectral signal identification by minimum error (H y S ime ) method, commonly used for signal subspace identification in remotely sensed hyperspectral images. Compared with the current implementations of this stage, the new algorithm for noise estimation relies on the reliable QR factorization, producing correct results even when operating with single-precision arithmetic. Additionally, our algorithm exhibits a lower computational cost, and it is highly parallel. The experiments on a multicore server, using two real hyperspectral scenes, expose that these theoretical advantages carry over to the practical results.

In 1979, P. Huard presented an efficient variant of the Gauss-Jordan elimination for the solution of linear systems. In particular, this alternative algorithm exhibits the same computational cost as the traditional LU-based solver, and is considerably cheaper than the Gauss-Jordan algorithm, but there exist no recent high performance implementations of the Gauss-Huard (GH) variant that allow a comparison of these approaches. In this paper we present a reliable GH solver for hybrid platforms equipped with conventional multi-core technology and a graphics processing unit (GPU). The experimental results show that the GH algorithm can beat high performance versions of the LU solver, from tuned libraries for CPU-GPU servers such as MAGMA, for problems of small to moderate scale.

Linear algebra operations arise in a myriad of scientific and engineering applications and, therefore, their optimization is targeted by a significant number of high performance computing (HPC) research efforts. In particular, the matrix multiplication and the solution of linear systems are two key problems with efficient implementations (or kernels) for a variety of high per- formance parallel architectures. For these specific prob- lems, leveraging the structure of the associated matrices often leads to remarkable time and memory savings, as is the case, e.g., for symmetric band problems. In this work, we exploit the ample hardware concurrency of many-core graphics processors (GPUs) to accelerate the solution of symmetric positive definite band linear systems, introducing highly tuned versions of the corre- sponding LAPACK routines. The experimental results with the new GPU kernels reveal important reductions of the execution time when compared with tuned imple- mentations of the same operations provided in Intel’s MKL. In addition, we evaluate the performance of the GPU kernels when applied to the solution of model or- der reduction problems and the associated matrix equa- tions. Ernesto Dufrechou and Pablo Ezzatti acknowledge the support from Programa de Desarrollo de las Ciencias Básicas, and Agencia Nacional de Investigación e Innovacioón, Uruguay. Enrique S. Quintana-Ortí was sup- ported by project TIN2011-23283 of the Ministry of Science and Competitiveness (MINECO) and EU FEDER, and project P1-1B2013-20 of the Fundació Caixa Castelló-Bancaixa and UJI.

The solution of large-scale Lyapunov equations is an important tool for the solution of several engineering problems arising in optimal control and model order reduction. In this work, we investigate the case when the coefficient matrix of the equations presents a band structure. Exploiting the structure of this matrix, we can achive relevant reductions in the memory requirements and the number of floating-point operations. Additionally, the new solver efficiently leverages the parallelism of CPU–GPU platforms. Furthermore, it is integrated in the lyapack library to facilitate its use. The new codes are evaluated on the solution of several benchmarks, exposing significant runtime reductions with respect to the original CPU version in lyapack. Ernesto Dufrechou and Pablo Ezzatti acknowledge the support from Programa de Desarrollo de las Ciencias Básicas, and Agencia Nacional de Investigación e Innovación of Uruguay. Enrique S. Quintana-Ortí was supported by project TIN2011-23283 of the Ministry of Science and Competitiveness (MINECO) and EU FEDER, and project P1-1B2013-20 of the Fundació Caixa Castelló-Bancaixa and UJI.