solution of linear equations using gaussian elimination

... 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 + 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 3N x N =b 3 ··· ... call 1- 800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 2. Solution of Linear...

Ngày tải lên: 15/12/2013, 04:15

... 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

... 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 A...

Ngày tải lên: 15/12/2013, 04:15

... case of a single right-hand side vector):    a  11 a  12 a  13 a  14 0 a  22 a  23 a  24 00a  33 a  34 000a  44    ·    x 1 x 2 x 3 x 4    =    b  1 b  2 b  3 b  4    (2.2.1) Here ... identity matrix),Gaussianeliminationandbacksubstitutionatfirstglancerequire 1 3 N 3 (matrix reduction) + 1 2 N 3 (right-hand side manipulations) + 1 2 N 3 (N...

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 ... case of a 4 ì 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 α 33 0 α 41 α 42 α 43 α 44   · ...

Ngày tải lên: 24/12/2013, 12:16

... 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 -52 1-43108 -5) Copyright (C) 1988-1992 ... += a[i][j]*x[j+k]; } } 54 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTI...

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 ... 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 ... matrices  a...

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 ... 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

... 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 ... call 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). A ⋅ x = b SVD solution  of A ⋅ x = c solutions of A ⋅ x =...

Ngày tải lên: 24/12/2013, 12:16

... multiply routine. 86 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-431 08- 5) Copyright (C) 1 988 -1992 by Cambridge ... long ijc[]) 80 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-431 0...

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 (C) 198 8- 199 2 by Cambridge ... 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 (C)...

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 NUM...

Ngày tải lên: 21/01/2014, 18:20

... Journal of Science, Mathematics - Physics 23 (2007) 201-209 Fully parallel methods for a class of linear partial differential-algebraic equations Vu Tien Dung ∗ Department of Mathematics, Mechanics, ... Albarreal, M.C. Calzada, J.L. Cruz, E. Fern ´ andez-Cara, M. Mari´n, Stability and Convergence of a Parallel Fractional Step Method for the Solution of Lin...

Ngày tải lên: 13/02/2014, 03:20

... ,k 2s ∈{0, 1, ,N}; this Annals of Mathematics Isomonodromy transformations of linear systems of difference equations By Alexei Borodin ISOMONODROMY TRANSFORMATIONS 1147 probability ... a polynomial of degree n −1. Lemma 3.2. A linear function z −B is a right divisor of A(z) if and only if A 0 B n + A 1 B n−1 + ···+ A n =0. Proof. See, e.g., [GLR]. IS...

Ngày tải lên: 14/02/2014, 17:20

... Objectives Introduction Gaussian elimination method Gaussian elimination procedure Programming exercise General information Title: Solution of linear equations using Gaussian elimination Teacher(s): Professor ... Solution of linear equations using Gaussian elimination FAQ Reference s SummaryInfo Resources Learning Objectives Introduction Gaussian elimi...

Ngày tải lên: 24/10/2014, 21:28