17.3 Relaxation Methods 765 XXXXX B XXXXX V B XXXXX V XXXXXXXXXX XXXXXXXXXX V ⊙ XXXXX X XXXX ⊙ XXXXXXXXXX B XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX V Permission is XXXXXXXXXX V B XXXXXXXXXX V XXXXXXXXXX V BB XXXXXXXXXX B XXXXXXXXXX V B .com or call 1-800-872- (including this one) granted fori XXXXXXXXXX V internet XXXXXXXXXX V B XXXXXXXXXX V B XXXXX 7423 (North America to any server computer, 1988-1992 by Cambridge University Press. from NUMERICAL RECIPES IN C: XXXXX B Figure 17.3.1.Matrix structure of a set of linear finite-difference equations (FDEs)with boundary conditions imposed at both endpoints.Here X represents a coefficient of the FDEs,V represents a t users to make one paper component of the unknown solution vector,and B is a component of the known right-hand side.Empty spaces represent zeros.The matrix equation is to be solved by a special form of Gaussian elimination. (See text for details.) is is copy for their Programs XX B XX 0 Copyright (C) 1 XX B 1 XX B 1 1 十 B 1 X 1 X B To order Numerical Recipes books or 1988-1992 by Numerical Recipes THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) 1 XX X B 1 1 B 1 X XX 1 B @cambridge.org(outside North America). Software. X B 1 XX B ying of machine visit website 1 V B 1 0 Figure 17.3.2.Target structure of the Gaussian elimination.Once the matrix of Figure 17.3.1 has been reduced to this form,the solution follows quickly by backsubstitution.17.3 Relaxation Methods 765 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X V V V V V V V V V V V V V V V V V V V V B B B B B B B B B B B B B B B B B B B B Figure 17.3.1. Matrix structure of a set of linear finite-difference equations (FDEs) with boundary conditions imposed at both endpoints. Here X represents a coefficient of the FDEs, V represents a component of the unknown solution vector, and B is a component of the known right-hand side. Empty spaces represent zeros. The matrix equation is to be solved by a special form of Gaussian elimination. (See text for details.) 1 1 1 X X X 1 X X X 1 1 1 1 X X X X X 1 X X X X X 1 1 1 1 X X X X X 1 1 1 1 X X X X X 1 X X X X X 1 V V V V V V V V V V V V V V V V V V V V B B B B B B B B B B B B B B B B B B B B X X X X X 1 Figure 17.3.2. Target structure of the Gaussian elimination. Once the matrix of Figure 17.3.1 has been reduced to this form, the solution follows quickly by backsubstitution