solving simultaneous equations algebraic method

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 17/12/2013, 15:17

... simulta- neous equations, the literature published during the 1960s and 1970s concentrated heavily on the sampling distributions of estimators and test statistics in single structural equations ... unidentifiable. Note that the reduced-form equations take the form YI = =,r,, + 01. r, = .&II,, + v,, when II,, = 0. The first of these equations corresponds to (3.36) in the text ... corresponds to (3.36) in the text when /3 = 0. EXACT SMALL SAMPLE THEORY IN THE SIMULTANEOUS EQUATIONS MODEL 456 P. C. B. Phillips the weights being determined by the exogenous...

Ngày tải lên: 25/01/2014, 07:20

Ngày tải lên: 17/03/2014, 08:20

Ngày tải lên: 27/06/2014, 18:20

... convergence, we use other methods, such as the parallel Jacobi method [5], the parallel SOR Red/Black [6,7,8,9] method. The parallel Jacobi method and Parallel SOR Red/Black method are implemented ... 12 December 2007 Abstract. This note deals with two fully parallel methods for solving linear partial differential- algebraic equations (PDAEs) of the form: Au t + B∆u = f(x, t) (1) where A is ... of proposed methods are discussed. Some numerical experiments on high-performance computers are also reported. Keywords: Differential -algebraic equation (DAE), partial differential -algebraic equation...

Ngày tải lên: 13/02/2014, 03:20

... 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 + ···+a 1N x N =b 1 a 21 x 1 + ... of equationsto be solved can bewritten as the N ìN set of equations (A T Ã A) Ã x =(A T Ãb)(2.0.4) where A T denotes the transpose of the matrix A. Equations (2.0.4) are called the normal equations ... as many 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...

Ngày tải lên: 15/12/2013, 04:15

... elimination is about as efficient as any other method. For solving sets of linear equations, Gauss-Jordan elimination produces both the solution of the equations for one or more right-hand side vectors b, ... Gauss-Jordan elimination should usually not be your method of first choice, either for solving linear equations or for matrix inversion. The decomposition methods in Đ2.3 are better. Why do we give you ... than the best alternative technique for solving a single linear set (Đ2.3). The methods principal strength is that it is as stable as any other direct method, perhaps even a bit more stable when...

Ngày tải lên: 15/12/2013, 04:15

... 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 Algebraic Equations Sample page from NUMERICAL ... needed, so we separate it off into its own routine rsolv. 98 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 ... numericalalgorithms involve solvinga successionof linear systems each of which differs only slightly from its predecessor. Instead of doing O(N 3 ) operations each time to solve the equations from scratch,...

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 ... two methods have identical efficiencies. BothGaussian eliminationand Gauss-Jordan eliminationshare thedisadvantage that all right-hand sides must be known in advance. The LU decomposition method in ... READING: Wilkinson, J.H. 1965, The Algebraic Eigenvalue Problem (New York:Oxford University Press). [1] Carnahan, B., Luther, H.A., and Wilkes, J.O. 1969, Applied Numerical Methods (New York: Wiley),...

Ngày tải lên: 24/12/2013, 12:16

... a ij (2.3.10) Equations (2.3.8)–(2.3.10) total N 2 equations for the N 2 + N unknown α’s and β’s (the diagonal being represented twice). Since the number of unknowns is greater than the number of equations, ... trade@cup.cam.ac.uk (outside North America). method. Only partial pivoting (interchange of rows) can be implemented efficiently. However this is enough to make the method stable. This means, incidentally, ... 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 IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

Ngày tải lên: 24/12/2013, 12:16

... (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 COMPUTING (ISBN 0-521-43108-5) Copyright ... (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 ... READING: Keller, H.B. 1968, Numerical Methods for Two-Point Boundary-Value Problems (Waltham, MA: Blaisdell), p. 74. Dahlquist, G., and Bjorck, A. 1974, Numerical Methods (Englewood Cliffs, NJ: Prentice-Hall), Example...

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 ... inverses of each other. Then the c’s can be obtained from the a’s by the following operations (compare equations 2.7.22 and 2.7.25): R 1 = Inverse(a 11 ) R 2 = a 21 ì R 1 R 3 = R 1 ì a 12 R 4 = a 21 ì...

Ngày tải lên: 24/12/2013, 12:16

... various names, including Schultz’s Method and Hotelling’s Method; seePanandReif [1] for references. In fact, equation (2.5.11) is simply the iterative Newton-Raphson method of root-nding (Đ9.4) applied ... but a second call to 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 ... and Bjorck, A. 1974, Numerical Methods (Englewood Cliffs, NJ: Prentice-Hall), Đ 5.5.6, p. 183. Forsythe, G.E., and Moler, C.B. 1967, Computer Solution of Linear Algebraic Systems (Engle- wood...

Ngày tải lên: 24/12/2013, 12:16

... for More Equations than Unknowns This situation will occur in Chapter 15, when we wish to find the least-squares solution to an overdetermined set of linear equations. In tableau, the equations to ... nonzero during the solution process, and for which storage must be reserved. Direct methods for solving sparse equations, then, depend crucially on the precise pattern of sparsity of the matrix. ... *g; g=s=scale=0.0; if(i<=m&&i!=n){ for (k=l;k<=n;k++) scale += fabs(a[i][k]); if (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...

Ngày tải lên: 24/12/2013, 12:16

... Gradient Method for a Sparse System So-called conjugate gradient methods provide a quite general means for solving the N ì N linear system A Ã x = b (2.7.29) The attractiveness of these methods ... our interest is in solving linear, but not necessarily positive definite or symmetric, equations, a different generalization is important, the biconjugate gradient method. This method does not, ... gradient method. This algorithm has been generalized in various ways for unsymmetric matrices. The generalized minimum residual method (GMRES; see [9,15] )is probably the most robust of these methods. Note...

Ngày tải lên: 24/12/2013, 12:16

... N) 2 operations, compared to N 2 for Levinson’s method. These methods are too complicated to include here. 90 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: ... always to compute 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 ... the desired answer only when N is reached. Levinson’s method is well documented in standard texts (e.g., [5] ). The useful fact that the method generalizes to the nonsymmetric case seems to be...

Ngày tải lên: 21/01/2014, 18:20

... can use it, Choleskydecomposition is about a factor of two faster than alternative methods for solving linear equations. Instead of seeking arbitrary lower and upper triangular factors L and U, ... 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 ... ) 2 operations, compared to N 2 for Levinson’s method. These methods are too complicated to include here. 90 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C:...

Ngày tải lên: 21/01/2014, 18:20

Ngày tải lên: 13/02/2014, 20:20