Tài liệu Solution of Linear Algebraic Equations part 2 ppt

... equation   a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44   ·     x 11 x 21 x 31 x 41      x 12 x 22 x 32 x 42      x 13 x 23 x 33 x 43      y 11 y 12 y 13 y 14 y 21 y 22 y 23 y 24 y 31 y 32 y 33 y 34 y 41 y 42 y 43 y 44     =     b 11 b 21 b 31 b 41      b 12 b 22 b 32 b 42...

Ngày tải lên: 15/12/2013, 04:15

... matrices,  a 11 a 12 a 21 a 22  ·  b 11 b 12 b 21 b 22  =  c 11 c 12 c 21 c 22  (2. 11.1) Eight, right? Here they are written explicitly: c 11 = a 11 × b 11 + a 12 × b 21 c 12 = a 11 × b 12 + a 12 × b 22 c 21 = a 21 × ... on.) Such a set of formulas was, in fact, discovered by Strassen [1] . The formulas are: Q 1 ≡ (a 11 + a 22 ) × (b 11 + b 22 )...

Ngày tải lên: 15/12/2013, 04:15

... 56 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5) Copyright (C) 1988-19 92 by Cambridge University ... feasible)? 2. 5 Iterative Improvement of a Solution to Linear Equations 55 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-...

Ngày tải lên: 24/12/2013, 12:16

... 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 2. Solution of Linear Algebraic Equations 2. 0 Introduction A set of linear algebraic equations ... this: a 11 x 1 + a 12 x 2 + a 13 x 3 + ···+a 1N x N =b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + ···+a 2N x N =b 2 a 31 x 1 + a 32 x 2 + a 33 x 3 + ···+a...

Ngày tải lên: 15/12/2013, 04:15

... 42 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5) Copyright (C) 1988-19 92 by Cambridge ... is x i = 1 a  ii   b  i − N  j=i+1 a  ij x j   (2. 2.4) The procedure defined by equation (2. 2.4) is called backsubstitution.Thecom- bination of Gaussian elimination and backsubs...

Ngày tải lên: 24/12/2013, 12:16

... β 22 β 23 β 24 00β 33 β 34 000β 44   =   a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44   (2. 3 .2) We can use a decomposition such as (2. 3.1) to solve the linear set A · x =(L·U)·x=L·(U·x)=b (2. 3.3) by ... case of a 4 × 4 matrix A, for example, equation (2. 3.1) would look like this:   α 11 000 α 21 α 22 00 α 31 α 32...

Ngày tải lên: 24/12/2013, 12:16

... elimination. dum=a[i][1]/a[k][1]; al[k][i-k]=dum; for (j =2; j<=mm;j++) a[i][j-1]=a[i][j]-dum*a[k][j]; a[i][mm]=0.0; } } } 52 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 1967, Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake,...

Ngày tải lên: 24/12/2013, 12:16

... Inverse(a 11 ) R 2 = a 21 × R 1 R 3 = R 1 × a 12 R 4 = a 21 × R 3 R 5 = R 4 − a 22 R 6 = Inverse(R 5 ) c 12 = R 3 × R 6 c 21 = R 6 × R 2 R 7 = R 3 × c 21 c 11 = R 1 − R 7 c 22 = −R 6 (2. 11.6) ... matrices  a 11 a 12 a 21 a 22  and  c 11 c 12 c 21 c 22  (2. 11.5) are inverses of each other. Then the c’s can be obtained from the a’s by the following ope...

Ngày tải lên: 24/12/2013, 12:16

... (scale) { 62 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5) Copyright (C) 1988-19 92 by Cambridge ... q.e.d. Figure 2. 6.1 summarizes our discussion of SVD thus far. 68 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE AR...

Ngày tải lên: 24/12/2013, 12:16

... j,jl,jm,jp,ju,k,m,n2,noff,inc,iv; float v; n2=ija[1]; Linear size of matrix plus 2. for (j=1;j<=n2 -2; j++) sb[j]=sa[j]; Diagonal elements. iindexx(ija[n2-1]-ija[1],(long *)&ija[n2-1],&ijb[n2-1]); Index ... 0. 0. 0. 2. 0. 0. 0. 6. 5.      (2. 7 .27 ) 74 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF S...

Ngày tải lên: 24/12/2013, 12:16