numerical solution of simultaneous linear algebraic equations

... 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 of the M equations is a linear ... “pointer to array of pointersto rows.” You might wish to review that section 34 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING...

Ngày tải lên: 15/12/2013, 04:15

... of N ì 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 ... Springer-Verlag). Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Johnson, L.W., and Riess, R.D. 1982, Numerical Analysis , 2nd ed. (Reading, ... 36 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...

Ngày tải lên: 15/12/2013, 04:15

... typical systems of linear equations. However, we will meet special cases where QR is the method of choice. 100 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES ... 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 ... purposes, because of its greater diagnostic capability in pathological cases.) Updating a QR decomposition Some numericalalgorithms involve solvinga successionof linear systems each of which differs...

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 ... 298. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Ralston, A., and Rabinowitz, P. 1978, A First Course in Numerical Analysis , 2nd ed. ... is called backsubstitution.Thecom- bination of Gaussian elimination and backsubstitution yields a solution to the set of equations. The advantage of Gaussian elimination and backsubstitutionover...

Ngày tải lên: 24/12/2013, 12:16

... 1967, Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New ... 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 Equations Sample page from NUMERICAL RECIPES ... (i.e., selection of a salubrious pivot element for the division in equation 2.3.13) is absolutely essential for the stability of Crout’s 50 Chapter 2. Solution of Linear Algebraic Equations Sample...

Ngày tải lên: 24/12/2013, 12:16

... 1967, Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New ... (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 SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... Johns Hopkins University Press), Đ 4.3. 50 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...

Ngày tải lên: 24/12/2013, 12:16

... 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 ... (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine- readable ... submatrices. Imagine doing the inversionof a very large matrix, of order N =2 m , recursively by partitions in half. At each step, halving the order doubles the number of inverse operations. But this...

Ngày tải lên: 24/12/2013, 12:16

... 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 ... verify convergence can be reassuring. 58 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 ... 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...

Ngày tải lên: 24/12/2013, 12:16

... North America). A ⋅ 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 ... making the same permutation of the columns of U,elementsofW,andcolumnsofV(or rows of V T ), or (ii) forming linear combinations of any columns of U and V whose corresponding elements of W happen to be ... throwing away one linear combination of the set of equations that we are trying to solve. The resolution of the paradox is that we are throwing away precisely a combination of equations that is...

Ngày tải lên: 24/12/2013, 12:16

... form the sequence of improved estimates x k+1 = x k + α k p k (2.7.37) 76 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... 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 ... before sending it to the matrix multiply routine. 86 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...

Ngày tải lên: 24/12/2013, 12:16

... 92 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 ... Vandermonde problems in double precision. 94 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 ... are too complicated to include here. 90 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...

Ngày tải lên: 21/01/2014, 18:20

... 1967, Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Đ19. [1] Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New ... for fast solution of the symmetric Toeplitz problem, by a bordering method,thatis, 98 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... equations (2.3.12)–(2.3.13), L ii =  a ii − i−1  k=1 L 2 ik  1/2 (2.9.4) and L ji = 1 L ii  a ij − i−1  k=1 L ik L jk  j = i +1,i+2, ,N (2.9.5) 92 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...

Ngày tải lên: 21/01/2014, 18:20

... collection of events, sigma-algebra A filtration E(X) expectation of X E(X |A) conditional expectation of X under A P (A) probability of A P (A |B) probability of A conditioned on B ∈ element of ∈ ... a small class of jump diffusion SDEs admits explicit solutions, it is important to construct discrete-time approximations. The focus of this monograph is the numerical solution of SDEs with jumps ... hardware devices and seems to provide solutions where no alternative is known. The focus of this book is on the numerical solution of stochastic differential equations (SDEs) with jumps via simulation...

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