Tài liệu Solution of Linear Algebraic Equations part 3 pdf

... case of a single right-hand side vector):a11a12a 13 a140 a22a 23 a2400a 33 a 34 000a44·x1x2x 3 x4=b1b2b 3 b4(2.2.1)Here ... Gaussian elimination.42Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... identitymatrix),Gaussianeliminationandbacksubstitutionatﬁrstglancerequire1 3 N 3 (matrixreduction) +12N 3 (right-hand side manipulations) +12N 3 (N backsubstitutions)=4 3 N 3 loop executions, which is more than the N 3 for Gauss-Jordan....

Tài liệu Solution of Linear Algebraic Equations part 12 pdf

... 102Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... a22) × (b21+ b22)(2.11 .3) 2.11 Is Matrix Inversion anN 3 Process?1 03 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 ... reducesthe process of matrix multiplication to order Nlog27instead of N 3 .What about all the extra additions in (2.11 .3) –(2.11.4)? Don’t they outweighthe advantage of the fewer multiplications?...

Tài liệu Solution of Linear Algebraic Equations part 1 docx

... a12x2+ a 13 x 3 + ···+a1NxN=b1a21x1+ a22x2+ a 23 x 3 + ···+a2NxN=b2a 31 x1+ a 32 x2+ a 33 x 3 + ···+a3NxN=b 3 ··· ···aM1x1+aM2x2+aM3x 3 +···+aMNxN= ... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Chapter 2. Solution of Linear Algebraic Equations 2.0 IntroductionA set of linear algebraic equations ... equations as unknowns, and there is a goodchance of solving for a unique solution set of xj’s. Analytically, there can fail tobe a unique solution if one or more of the M equations is a linear...

Tài liệu Solution of Linear Algebraic Equations part 2 ppt

... equationa11a12a 13 a14a21a22a 23 a24a 31 a 32 a 33 a 34 a41a42a 43 a44·x11x21x 31 x41x12x22x 32 x42x 13 x 23 x 33 x 43 y11y12y 13 y14y21y22y 23 y24y 31 y 32 y 33 y 34 y41y42y 43 y44=b11b21b 31 b41b12b22b 32 b42b 13 b 23 b 33 b 43 1000010000100001(2.1.1)Here ... equationa11a12a 13 a14a21a22a 23 a24a 31 a 32 a 33 a 34 a41a42a 43 a44·x11x21x 31 x41x12x22x 32 x42x 13 x 23 x 33 x 43 y11y12y 13 y14y21y22y 23 y24y 31 y 32 y 33 y 34 y41y42y 43 y44=b11b21b 31 b41b12b22b 32 b42b 13 b 23 b 33 b 43 1000010000100001(2.1.1)Here ... the solution set, as one sees instantly from (2.1.2). 38 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright...

Tài liệu Solution of Linear Algebraic Equations part 11 ppt

... solve linear systems. In many applications only the part (2.10.4) of the algorithm is needed, so we separate it off into its own routine rsolv.100Chapter 2. Solution of Linear Algebraic Equations Sample ... 98Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... typical systems of linear equations. However, we willmeet special cases where QR is the method of choice.2.10 QR Decomposition99Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Tài liệu Solution of Linear Algebraic Equations part 4 docx

... equation (2 .3. 1) would look like this:α11000α21α2200α 31 α 32 α 33 0α41α42α 43 α44·β11β12β 13 β140 β22β 23 β2400β 33 β 34 000β44=a11a12a 13 a14a21a22a 23 a24a 31 a 32 a 33 a 34 a41a42a 43 a44(2 .3. 2)We ... β22β 23 β2400β 33 β 34 000β44=a11a12a 13 a14a21a22a 23 a24a 31 a 32 a 33 a 34 a41a42a 43 a44(2 .3. 2)We can use a decomposition such as (2 .3. 1) to solve the linear setA · x =(L·U)·x=L·(U·x)=b (2 .3. 3)by ﬁrst solving ... αii(equation 2 .3. 11) are not stored at all.] In brief,Crout’s method ﬁlls in the combined matrix of α’s and β’s,β11β12β 13 β14α21β22β 23 β24α 31 α 32 β 33 β 34 α41α42α 43 β44(2 .3. 14)by...

Tài liệu Solution of Linear Algebraic Equations part 5 docx

... 50Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... a[i][j-1]=a[i][j]-dum*a[k][j];a[i][mm]=0.0;}}}54Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... Cambridge University Press).2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations that is tridiagonal, that is, hasnonzero elements only on the...

Tài liệu Solution of Linear Algebraic Equations part 6 pptx

... (2.5.2) givesA · δx = δb (2.5 .3) 56Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 ... to obtain greater precision for the solution of a linear set than the precision of your computer’s ﬂoating-point word. Unfortunately, forlarge sets of linear equations, it is not always easy to ... decomposition is not feasible)?58Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by...

Tài liệu Solution of Linear Algebraic Equations part 7 docx

... makingthe same permutation of the columns of U,elementsofW,andcolumnsofV(orrows of VT), or (ii) forming linear combinations of any columns of U and V whosecorresponding elements of W happen to be ... also be aware of some of the special sparse forms that occur in thesolutionof partial differential equations in two or more dimensions. See Chapter 19.If your particular pattern of sparsity is ... δkn1 ≤ k ≤ N1 ≤ n ≤ N(2.6 .3) 68Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992...

Tài liệu Solution of Linear Algebraic Equations part 8 docx

... specially, because thatparticular type of linear system admits a solution in only of order N operations,rather than of order N 3 for the general linear problem. When such particular typesexist, ... special order of interchanges and eliminations,90Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright ... also be aware of some of the special sparse forms that occur in thesolutionof partial differential equations in two or more dimensions. See Chapter 19.If your particular pattern of sparsity is...

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