The symmetric-Toeplitz linear system problem in parallel

[EN] Many algorithms exist that exploit the special structure of Toeplitz matrices for solving linear systems. Nevertheless, these algorithms are difficult to parallelize due to its lower computational cost and the great dependency of the operations involved that produces a great communication cost. The foundation of the parallel algorithm presented in this paper consists of transforming the Toeplitz matrix into a another structured matrix called Cauchy¿like. The particular properties of Cauchy¿like matrices are exploited in order to obtain two levels of parallelism that makes possible to highly reduce the execution time. The experimental results were obtained in a cluster of PC¿s.Supported by Spanish MCYT and FEDER under Grant TIC 2003-08238-C02-02Alonso-Jordá, P.; Vidal Maciá, AM. (2005). The symmetric-Toeplitz linear system problem in parallel. Computational Science -- ICCS 2005,Pt 1, Proceedings. 3514:220-228. https://doi.org/10.1007/11428831_28S2202283514Sweet, D.R.: The use of linear-time systolic algorithms for the solution of toeplitz problems. k Technical Report JCU-CS-91/1, Department of Computer Science, James Cook University, Tue, 23 April 1996 15, 17, 55 GMT (1991)Evans, D.J., Oka, G.: Parallel solution of symmetric positive definite Toeplitz systems. Parallel Algorithms and Applications 12, 297–303 (1998)Gohberg, I., Koltracht, I., Averbuch, A., Shoham, B.: Timing analysis of a parallel algorithm for Toeplitz matrices on a MIMD parallel machine. Parallel Computing 17, 563–577 (1991)Gallivan, K., Thirumalai, S., Dooren, P.V.: On solving block toeplitz systems using a block schur algorithm. In: Proceedings of the 23rd International Conference on Parallel Processing, Boca Raton, FL, USA, vol. 3, pp. 274–281. CRC Press, Boca Raton (1994)Thirumalai, S.: High performance algorithms to solve Toeplitz and block Toeplitz systems. Ph.d. th., Grad. College of the U. of Illinois at Urbana–Champaign (1996)Alonso, P., Badía, J.M., Vidal, A.M.: Parallel algorithms for the solution of toeplitz systems of linear equations. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2004. LNCS, vol. 3019, pp. 969–976. Springer, Heidelberg (2004)Anderson, E., et al.: LAPACK Users’ Guide. SIAM, Philadelphia (1995)Blackford, L., et al.: ScaLAPACK Users’ Guide. SIAM, Philadelphia (1997)Alonso, P., Badía, J.M., González, A., Vidal, A.M.: Parallel design of multichannel inverse filters for audio reproduction. In: Parallel and Distributed Computing and Systems, IASTED, Marina del Rey, CA, USA, vol. II, pp. 719–724 (2003)Loan, C.V.: Computational Frameworks for the Fast Fourier Transform. SIAM Press, Philadelphia (1992)Heinig, G.: Inversion of generalized Cauchy matrices and other classes of structured matrices. Linear Algebra and Signal Proc., IMA, Math. Appl. 69, 95–114 (1994)Gohberg, I., Kailath, T., Olshevsky, V.: Fast Gaussian elimination with partial pivoting for matrices with displacement structure. Mathematics of Computation 64, 1557–1576 (1995)Alonso, P., Vidal, A.M.: An efficient and stable parallel solution for symmetric toeplitz linear systems. TR DSIC-II/2005, DSIC–Univ. Polit. Valencia (2005)Kailath, T., Sayed, A.H.: Displacement structure: Theory and applications. SIAM Review 37, 297–386 (1995

RICORS2040 : The need for collaborative research in chronic kidney disease

Chronic kidney disease (CKD) is a silent and poorly known killer. The current concept of CKD is relatively young and uptake by the public, physicians and health authorities is not widespread. Physicians still confuse CKD with chronic kidney insufficiency or failure. For the wider public and health authorities, CKD evokes kidney replacement therapy (KRT). In Spain, the prevalence of KRT is 0.13%. Thus health authorities may consider CKD a non-issue: very few persons eventually need KRT and, for those in whom kidneys fail, the problem is 'solved' by dialysis or kidney transplantation. However, KRT is the tip of the iceberg in the burden of CKD. The main burden of CKD is accelerated ageing and premature death. The cut-off points for kidney function and kidney damage indexes that define CKD also mark an increased risk for all-cause premature death. CKD is the most prevalent risk factor for lethal coronavirus disease 2019 (COVID-19) and the factor that most increases the risk of death in COVID-19, after old age. Men and women undergoing KRT still have an annual mortality that is 10- to 100-fold higher than similar-age peers, and life expectancy is shortened by ~40 years for young persons on dialysis and by 15 years for young persons with a functioning kidney graft. CKD is expected to become the fifth greatest global cause of death by 2040 and the second greatest cause of death in Spain before the end of the century, a time when one in four Spaniards will have CKD. However, by 2022, CKD will become the only top-15 global predicted cause of death that is not supported by a dedicated well-funded Centres for Biomedical Research (CIBER) network structure in Spain. Realizing the underestimation of the CKD burden of disease by health authorities, the Decade of the Kidney initiative for 2020-2030 was launched by the American Association of Kidney Patients and the European Kidney Health Alliance. Leading Spanish kidney researchers grouped in the kidney collaborative research network Red de Investigación Renal have now applied for the Redes de Investigación Cooperativa Orientadas a Resultados en Salud (RICORS) call for collaborative research in Spain with the support of the Spanish Society of Nephrology, Federación Nacional de Asociaciones para la Lucha Contra las Enfermedades del Riñón and ONT: RICORS2040 aims to prevent the dire predictions for the global 2040 burden of CKD from becoming true