Finally a cheap approximaThis of the eimpliesthat is proposed.
The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method.
The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form.
Most importantly, it offers second-order accuracy even on meshes that are not smooth, rigorously treats material discontinuities, and has a symmetric positive-definite coefficient matrix.
Most importantly, it offers second-order accuracy on reasonably well-behaved nonsmooth meshes, rigorously treats material discontinuities, and has a symmetric positive-definite coefficient matrix.
However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix.
Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed.
As regard to the obtained results, a definite region for coefficient of performance of the refrigerator and a definite region for the thermal efficiency of the heat engine of the duplex Stirling are identified.
There was a definite positive relationship (correlation coefficient: 0.73, significance level: < 0.01) between the VNT titer of the dam and the VNT titer of the corresponding calf (age ≤ 30 days) of 13 dam-calf combinations sampled on the same day: the higher the VNT titer of the dam, the higher the VNT titer (maternal antibodies) of the calf.
Moreover, the symmetric positive-definite property of the coefficient matrix on an (N−1 -dimensional hyperplaN−1 -dimensional fundamental importance to thyperplanesedness of the models — can be proved equivalent to some physical condition for pairwhichsurface tensisns.
In what follows we discuss an example built on the global NPC space (of all dimensional positive definite matrices with real coefficients), when endowed with the trace metric, (4.1).
