1549301742-The_Theory_of_Difference_Schemes__Samarskii

736 Methods for Solving Grid Equations with parameters ( rk> wiJ (29) Tk+l = (Awki wd ' Estimate (29) is still valid in that ...

Other iterative inethocls 737 yielding 11 s 112 ~ 1 - 2 T fl + T2 f1 f2. Having stipulated the 1ninimum condition for the preced ...

738 where Methods for Solving Grid Equations 1-~ Po= l + ~, l, c -- /1 , /2 so that T = T 0 B. The second sununand on the right- ...

Other iterative inethods vVhen providing current nrnnipulations with 2 2 1 - p2 + a 2 = 1 - p2 + x ( 1 - po ) o o 1 _ x2 1 - PZ ...

740 Methods for Solving Grid Equations provided that conditions (34) hold. The number n of iterations for doing so is no less th ...

Other iterative methods^741 (for more detail see Section 2, formula (14)) governing the minimum con- dition for 11 rk+l 112. No ...

742 Methods for Solving Grid Equations Let now R = R* > 0 be a regularizer such that c 1 R < A < c 2 R, c 1 > 0. Kno ...

Other iterative 1nethods 743 where w is the exact solution to the equation Rw resolving operator subject to the relations rk and ...

744 Methods for Solving Grid Equations If R = R1 + R2, R:, =Ru:> 0 and R1 R2 = R2 Ri ADNI frmn Section 4, items 2-3 inay be e ...

Symbols wh = {x; = ih, h > 0, i = 1,2, ... ,N - 1, hN = l} - an equidistant (uniforn1) grid on the interval (0, /); wh = {x; ...

746 __ = 2_ ( Yi+1 - Yi _ Yi - Yi-1). Yxx Ji. I h· 1.+l h· I ' A list of inner products and associated norrns on a grid: N-l (y, ...

Symbols A* - adjoint operator; A-^1 - inverse operator; S - transition operator frmn one layer to another; T - resolving operato ...

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Concluding Remarks In concluding this book we give a brief con1mentary regarding the main results forth in the foregoing. In ord ...

750 Concluding Remarks should cause no confusion. This n1ethod was independently proposed by 1nany authors in the early fifties. ...

Concluding Ren1arks 751 role in the further recognition and establish1nent of convergence of homo- geneous difference schemes wi ...

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References Akhiezer, N. and Glazman, I. ( 1966) The Theory of Linear Operators in Hilbert Space. Nauka: Moscow (in Russian). Ale ...

754 References Berezanskij, Yu. (1968) Expansions in Eigenfunctions of Self-Adjoint Op- erator. AMS: Providence, RI. Bitsadze, A ...

References 755 Golant, E. (1978) On conjugate fa111ilies of cliffe1·ence schen1es for equations of parabolic type with lowe1· me ...