Evaluation of the performance of inexact GMRES

AbstractThe inexact GMRES algorithm is a variant of the GMRES algorithm where matrix–vector products are performed inexactly, either out of necessity or deliberately, as part of a trading of accuracy for speed. Recent studies have shown that relaxing matrix–vector products in this way can be justified theoretically and experimentally. Research, so far, has focused on decreasing the workload per iteration without significantly affecting the accuracy. But relaxing the accuracy per iteration is liable to increase the number of iterations, thereby increasing the overall runtime, which could potentially end up being greater than that of the exact GMRES if there were not enough savings in the matrix–vector products. In this paper, we assess the benefit of the inexact approach in terms of actual CPU time derived from realistic problems, and we provide cases that provide instructive insights into results affected by the build-up of the inexactness. Such information is of vital importance to practitioners who need to decide whether switching their workflow to the inexact approach is worth the effort and the risk that might come with it. Our assessment is drawn from extensive numerical experiments that gauge the effectiveness of the inexact scheme and its suitability for use in addressing certain problems, depending on how much inexactness is allowed in the matrix–vector products

Performance evaluation of inexact GMRES

Iterative methods are aimed at sparse linear systems that arise in many applications (e.g., PDEs, biology, computer science, technology, engineering, etc). These applications give rise to matrices that differ in terms of structure and characteristics, and these ultimately impact the solvers. The Generalized Minimal Residual Method (GMRES) is a widely used solver due to its robustness. The inexact GMRES algorithm is a variant of the GMRES algorithm where matrix-vector products are performed inexactly, either out of necessity or deliberately, in view of trading accuracy for speed. Recent studies have shown that relaxing matrix-vector products this way can be justified theoretically and experimentally. Research so far has focused on decreasing the workload per iteration without significantly affecting the accuracy. But relaxing the accuracy per iteration is susceptible to increase the number of iterations, thereby increasing the overall runtime, which could potentially end up greater than that of the exact GMRES if there were not enough savings in the matrix-vector products. In this dissertation, we assess the benefit of the inexact approach in terms of actual CPU time derived from realistic problems, and we provide cases that shed instructive insights into results affected by the buildup of the inexactness. Such information is of vital importance to practitioners who need to decide if switching their vested work-flow to the inexact approach is worth the effort and the risk that might come with it. Our assessment is drawn from extensive numerical experiments on the Alabama Supercomputing Facility that gauge the effectiveness of the inexact scheme and its suitability to certain problems depending on how much inexactness is allowed in the matrix-vector products. We present many different applications throughout this dissertation and we show different structures and characteristics of matrices which are useful in the sense that linear system solvers sometimes do not converge to the correct solution if the matrices do not have specific properties. We apply some incomplete preconditioning techniques to our inexact scheme and we show that we could accelerate the convergence or even recover convergence that was lost from the restarted GMRES

Tumor necrosis factor-like weak inducer of apoptosis (TWEAK) promotes glioblastoma cell chemotaxis via Lyn activation

Daya tarik wisata religi Indonesia merupakan anugerah yang dimiliki bangsa Indonesia, demikian keragaman budaya dengan potensi yang demikian sempurna. Pengembangan pariwisata religi dapat memberikan manfaat sebesar-besarnya bagi pembangunan, maka dalam pelaksanaannya dibutuhkan strategi yang terencana dan sistematis agar kepuasan serta loyalitas pengunjung dapat terbentuk. Penelitian ini merupakan penelitian lapangan (field research) dengan pendekatan kuantitatif. Data yang digunakan adalah data primer dan sekunder dengan metode survei melalui penyebaran kuesioner. Terdapat tiga variabel independen dalam penelitian ini yaitu (X1) kualitas layanan syariah, (X2) nilai-nilai Islam, dan (X3) citra destinasi. Variabel dependen (Y1) dalam penelitian ini adalah kepuasan pengunjung. Sedangkan variabel mediasi (Y2) adalah loyalitas. Populasi dalam penelitian ini adalah seluruh pengunjung atau peziarah wisata Masjid Agung Demak dalam kurun waktu satu tahun terakhir. Teknik pengambilan sampel dilakukan dengan purposive sampling. Pengumpulan data dalam penelitian ini dilakukan dengan membagikan kuesioner sejumlah 167 kepada para responden. Penelitian ini menggunakan alat analisis SEM-PLS dengan bantuan program WarpPLS 3.0. Hasil penelitian ini menunjukkan bahwa: (1) kualitas layanan syariah tidak berpengaruh terhadap loyalitas dengan koefisien ß=0,03 dan p=0,39 (2) nilai-nilai Islam berpengaruh positif dan signifikan secara langsung terhadap loyalitas dengan koefisien ß=0,34 dan p<0,01 (3) citra destinasi berpengaruh positif dan signifikan secara langsung terhadap loyalitas dengan koefisien ß=0,38 dan p<0,01 (4) Kualitas layanan syariah tidak berpengaruh terhadap kepuasan pengunjung dengan koefisien ß=0,16 dan p=0,1 (5) nilai-nilai Islam tidak berpengaruh terhadap kepuasan pengunjung dengan koefisien ß=0,12 dan p=0,07 (6) citra destinasi berpengaruh positif dan signifikan secara langsung terhadap kepuasan pengunjung dengan koefisien ß=0,64 dan p<0,01 (7) kepuasan pengunjung berpengaruh positif dan signifikan terhadap loyalitas dengan koefisien ß=0,24 dan p<0,01 (8) kepuasan pengunjung tidak memediasi hubungan antara kualitas layanan syariah dan loyalitas ditunjukkan pada model direct dan indirect tidak signifikan p=0,39 dan p=0,47 (9) kepuasan pengunjung tidak memediasi hubungan antara nilai-nilai Islam dan loyalitas ditunjukkan pada model direct dan indirect koefisien naik dari ß=0,34 menjadi ß=0,35 (10) kepuasan pengunjung memediasi sebagian hubungan antara citra destinasi dan loyalitas dengan koefisien turun dari ß=0,38 menjadi ß=0,26 serta tetap signifikan p<0,01

TWEAK, via its receptor Fn14, is a novel regulator of mesenchymal progenitor cells and skeletal muscle regeneration

Inflammation participates in tissue repair through multiple mechanisms including directly regulating the cell fate of resident progenitor cells critical for successful regeneration. Upon surveying target cell types of the TNF ligand TWEAK, we observed that TWEAK binds to all progenitor cells of the mesenchymal lineage and induces NF-κB activation and the expression of pro-survival, pro-proliferative and homing receptor genes in the mesenchymal stem cells, suggesting that this pro-inflammatory cytokine may play an important role in controlling progenitor cell biology. We explored this potential using both the established C2C12 cell line and primary mouse muscle myoblasts, and demonstrated that TWEAK promoted their proliferation and inhibited their terminal differentiation. By generating mice deficient in the TWEAK receptor Fn14, we further showed that Fn14-deficient primary myoblasts displayed significantly reduced proliferative capacity and altered myotube formation. Following cardiotoxin injection, a known trigger for satellite cell-driven skeletal muscle regeneration, Fn14-deficient mice exhibited reduced inflammatory response and delayed muscle fiber regeneration compared with wild-type mice. These results indicate that the TWEAK/Fn14 pathway is a novel regulator of skeletal muscle precursor cells and illustrate an important mechanism by which inflammatory cytokines influence tissue regeneration and repair. Coupled with our recent demonstration that TWEAK potentiates liver progenitor cell proliferation, the expression of Fn14 on all mesenchymal lineage progenitor cells supports a broad involvement of this pathway in other tissue injury and disease settings