Tài liệu Solution of Linear Algebraic Equations part 6 pptx

... improved solution x. 2.5 Iterative Improvement of a Solution to Linear Equations Obviously it is not easy to obtain greater precision for the solution of a linear set than the precision of your ... 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 ... 1974,...

Ngày tải lên: 24/12/2013, 12:16

... trade@cup.cam.ac.uk (outside North America). Chapter 2. Solution of Linear Algebraic Equations 2.0 Introduction A set of linear algebraic equations looks like this: a 11 x 1 + a 12 x 2 + a 13 x 3 + ... equations as unknowns, and there is a good chance of solving for a unique solution set of x j ’s. Analytically, there can fail to be a unique solution if one or more...

Ngày tải lên: 15/12/2013, 04:15

... case of N × N matrices, with M sets of right-hand side vectors, in completely analogous fashion. The routine implemented below is, of course, general. 38 Chapter 2. Solution of Linear Algebraic Equations Sample ... G.E., and Moler, C.B. 1 967 , Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall). Wilkinson, J.H., and Reinsch, C. 1971,...

Ngày tải lên: 15/12/2013, 04:15

... 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. 98 Chapter 2. Solution of Linear Algebraic Equations Sample ... not used for typical systems of linear equations. However, we will meet special cases where QR is the method of choice. 100 Chapter 2. Solution of Linear Alg...

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 ... Sciences (New York: McGraw-Hill), Program B-2, p. 298. Westlake, J.R. 1 968 , A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Ralston, A., and Rabinowitz, P. 1978, A ....

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... 1 967 , Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1 968 , A Handbook of Numerical Matrix Inversion and Solution of ... (i=j;i<=n;i++) { This is i = j of equation (2.3.12) and i = j +1 N of equation (2.3.13).sum=a[i][j]; for (k=1;k<j;k++) 44 Chapter 2. Solution of Linear Algebraic...

Ngày tải lên: 24/12/2013, 12:16

... 1 967 , Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1 968 , A Handbook of Numerical Matrix Inversion and Solution of ... (j=LMAX(1,1-k);j<=tmploop;j++) b[i] += a[i][j]*x[j+k]; } } 54 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF...

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... 104 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 ... 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) ... divisions in all! So divisions don’t dominate in the...

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... x = b SVD solution  of A ⋅ x = c solutions of A ⋅ x = c′ solutions of A ⋅ x = d null space of A  SVD solution of A ⋅ x = d range of A d c (b) (a) A x b c′ Figure 2 .6. 1. (a) A ... b  =0, 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

... case of a tridiagonal matrix was treated specially, because that particular type of linear system admits a solution in only of order N operations, rather than of order N 3 for the general linear ... Package [6] . You should be aware that the special order of interchanges and eliminations, 84 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERIC...

Ngày tải lên: 24/12/2013, 12:16