1549301742-The_Theory_of_Difference_Schemes__Samarskii

716 Methods for Solving Grid Equations and Ct= /3 = 1 for .\(Ai)= ~ 1 , .\(A2) = ~ 2 , the constants p, q, r, T) are found by th ...

Iterative alternating direction methods Ai = ~A~, A2 = ~A~, wC1l = ~r(ll and wC^2 l rC^1 ) = rC^2 ) = T under the condition wC1l ...

718 Methods for Solving Grid Equations Having involved vk = (E + w 2 A 2 ) zA. with furter e!in1ination of zk+in from (18), we d ...

Iterative alternating direction methods 719 Along these lines, it is worth noting that we are still in the framework of the gene ...

720 Methods for Solving Grid Equations thereby completing the task of motivating the desired minimum. Via transforms (9)-(10) av ...

Iterative alternating direction rnethods 721 In order to understand the nature of this a little better, we refer to a model prob ...

722 Methods for Solving Grid Equations Factorized iteration sche111es and ADM. The main idea behind this ap- proach is connecte ...

Iterative alternating direction methods 723 We learn from Section 4 the values of paran1eters w 1 and w 2 for which the minimum ...

724 Methods for Solving Grid Equations When the operator R happens to be a regularizer for the operator A, that is, c 1 R < A ...

Iterative alternating direction rnethods 725 Remark 1 Frmn such reasoning it seems clear that ADM with variable parameters is eq ...

726 Methods for Solving Grid Equations helps clarify what is clone. As a matter of fact, searching for ~h+i amounts to successiv ...

Iterative alternating direction methods 727 In trying to solve the equation Au = f the iterative ADM with itera- tion parameter ...

728 Methods for Solving Grid Equations as required. By virtue of (37) it is plain to establish the relations Here the parameter ...

Other iterative methods^729 10.5 OTHER ITERATIVE METHODS Three-layer iteration sche111es. So far we have consicierecl two-layer ...

730 Methods for Solving Grid Equations and the parameter T should be so chosen as to minimize the norn1 115'11. We now know fror ...

Other iterative 1nethods 731 2p" Comparison of (8) with the resulting expression for qn =^12 , valid for 1 + P1 n Chebyshev's sc ...

732 Methods for Solving Grid Equations The minimal residual method. Until now the bounds / 1 and / 2 of the operator A were kno ...

Other iterative methods^733 Adopting those ideas to the case of a. non-self-adjoint opera.tor A, we derive from the foregoing th ...

734 Methods for Solving Grid Equations The forthcoming substitutions xk = B^112 yk> C = B-^112 AB-^112 and cp = B-^1!^2 fallo ...

Other iterative 1nethods 735 Having squared their norms, we find that (25) under the above condition 1nin II vk+l 112. The argum ...