review of linear algebra

... 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 + ... “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 ... consists of a particular solution x p added to any linear combination of (typically) N − M vectors (which are said to be in the nullspace of the matrix A). The task of finding the solution space of...

Ngày tải lên: 15/12/2013, 04:15

... Moler, C.B. 1967, Computer Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall). Wilkinson, J.H., and Reinsch, C. 1971, Linear Algebra ,vol.IIof Handbook for Automatic Com- putation (New ... row in A by a linear combination of itself and any other row, as long as we do the same linear combination of the rows of the b’s and 1 (which then is no longer the identity matrix, of course). • ... of this procedure, however, is thatthechoice of pivotwilldepend on the originalscaling of the equations. If we take the third linear equation in our original set and multiply it by a factor of...

Ngày tải lên: 15/12/2013, 04:15

... used to 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 ... it is 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 Algebraic Equations Sample page from ... Reinsch, C. 1971, Linear Algebra ,vol.IIof Handbook for Automatic Com- putation (New York: Springer-Verlag), Chapter I/1. Gill, P.E., Murray, W., and Wright, M.H. 1991, Numerical Linear Algebra and...

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) ... 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 ... increasing numbers of predictable zeros reduce the count to one-third), and 1 2 N 2 M times, respectively. Each backsubstitution of a right-hand side is 1 2 N 2 executions of a similar loop (one multiplication...

Ngày tải lên: 24/12/2013, 12:16

... modify the loop of the above fragment and (e.g.) divide by powers of ten, to keep track of the scale separately, or (e.g.) accumulate the sum of logarithms of the absolute values of the factors ... 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 ... Pivoting (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 (C) ... limitations of bandec, and the above routine does take advantage of the opportunity. In general, when TINY is returned as a diagonal element of U, then the original matrix (perhaps as modified by roundoff...

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) ... 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 ... complicated nature of the recursive Strassen algorithm, you will find that LU decomposition is in no immediate danger of becoming obsolete. If, on the other hand, you like this kind of fun, then try...

Ngày tải lên: 24/12/2013, 12:16

... 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 computer’s floating-point ... n] of the linear set of equations A · X = B.Thematrix a[1 n][1 n] , and the vectors b[1 n] and x[1 n] are input, as is the dimension n . Also input is alud[1 n][1 n] ,theLU decomposition of a as ... 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 (C)...

Ngày tải lên: 24/12/2013, 12:16

Ngày tải lên: 24/12/2013, 12:16

Ngày tải lên: 24/12/2013, 12:16

Ngày tải lên: 21/01/2014, 18:20

Ngày tải lên: 21/01/2014, 18:20

Ngày tải lên: 12/05/2014, 08:41

Ngày tải lên: 13/05/2014, 12:24

Ngày tải lên: 17/01/2014, 04:20

Ngày tải lên: 13/02/2014, 03:20

Ngày tải lên: 22/06/2014, 19:20

Ngày tải lên: 28/06/2014, 19:20

... the management of patients have a sound grasp of at least the basics of statistical methods. Unfortunately, in practice this is often not true, with many relying on distant memories of poorly understood ... fields of medicine but is often poorly understood and incorrectly applied. Critical Care is therefore launching a series of articles aimed at providing a simple introduction or refresher to some of ... texts Editorial Introducing the Critical Care Forum ’s ongoing review of medical statistics Elise Whitley* and Jonathan Ball † *Lecturer in Medical Statistics, University of Bristol, Bristol, UK † Lecturer in Intensive...

Ngày tải lên: 25/10/2012, 10:45