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Computational mathematics have many tools to solve the large systems of equations which may be linear or nonlinear. Iterative methods are used to solve the nonsymmetric definite system of linear equations like Krylov methods. Linear systems with multiple right-hand sides find application in many areas of engineering and science. Considering generality and indefiniteness, Krylov subspace methods are frequently used for such problems. However, problem with system with multiple right-hand side vectors requires constructing subspace for every right-hand side. GMRES produces Ritz vectors, approximation to eigenvectors during iterations. These Ritz values, recycled vectors are used in Krylov solve while solving system with second and subsequent right-hand side vectors. This is applied as a deflation preconditioner to GMRES. The numerical results show that the computational time, residuals and number of iterations is reduced as compare to simple GMRES. Deflation technique with Ritz vectors is not expensive as compare to the GMRES and as well as exact eigenvectors deflations.

The objective of this paper is to model and study the impact of high temperature on mortality in Pakistan. For this purpose, we have used mortality and climate data consisting of maximum temperature, variation in monthly temperature, average rainfall, humidity, dewpoint, as well as average air pressure in the country over the period from 2000 to 2019. We have used the Generalized Linear Model with Quasi-Poisson link function to model the number of deaths in the country and to assess the impact of maximum temperature on mortality. We have found that the maximum temperature in the country has a significant impact on mortality. The number of deaths in Pakistan increases as the maximum temperature increases. We found that, as the maximum temperature increase beyond 30 °C, mortality increases significantly. Our results indicate that mortality increases by 27% when the maximum temperature in the country increases from medium category to a very high level. Similarly, the number of deaths in the country increases by 11% when the temperature increases from medium temperature to high level. Furthermore, our study found that when the maximum temperature in the country decreases from a medium level to a low level, the number of deaths in the country decreases by 23%. This study does not consider the impact of other factors on mortality, such as age, medical conditions, gender, geographical location, as well as variability of temperature across the country.