Linear algebraic groups borel A

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Ngày tải lên: 13/05/2014, 12:22

... to 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 + ... to know about the tasks that have been defined above. In many cases you will have no alternative but to use sophisticated black-box program packages. Several good ones are ava...

Ngày tải lên: 15/12/2013, 04:15

... trade@cup.cam.ac.uk (outside North America). Elimination on Column-Augmented Matrices Consider the linear matrix 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...

Ngày tải lên: 15/12/2013, 04:15

... 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 Optimization ,vol.1 (Redwood ... n] and qt[1 n][1 n] , carry out a Jacobi rotation on rows i and i +1 of each matrix. a and b are the parameters of the rotation: cos θ = a/ √ a 2 + b 2 , sin θ = b/...

Ngày tải lên: 15/12/2013, 04:15

... the diagonal and above (say) remain nontrivial. Let us now see what advantages accrue. Suppose that in doing Gauss-Jordan elimination, as described in §2.1, we at each stage subtract away rows ... elimination thus has about a factor three advantage over Gauss-Jordan. (We could reduce this advantage to a factor 1.5 by not computing the inverse matrix as part of the Gauss-Jordan scheme.) Fo...

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 · x =(L·U)·x=L·(U·x)=b ... Applications Suppose we are able to write the matrix A as a product of two matrices, L · U = A (2.3.1) where L is lowe...

Ngày tải lên: 24/12/2013, 12:16

... one that occurs frequently. Also common are systems that are band diagonal,withnonzero elements only along a few diagonal lines adjacent to the main diagonal (above and below). For tridiagonal sets, ... Press). 2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations that is tridiagonal, that is, has nonzero elements only on the diagonal pl...

Ngày tải lên: 24/12/2013, 12:16

... J.H., and Reinsch, C. 1971, Linear Algebra ,vol.IIof Handbook for Automatic Com- putation (New York: Springer-Verlag), Chapter I/8. [1] Golub, G.H., and Van Loan, C.F. 1989, Matrix Computations , ... that the matrices  a 11 a 12 a 21 a 22  and  c 11 c 12 c 21 c 22  (2.11.5) are inverses of each other. Then the c’s can be obtained from the a s by the following operations (compar...

Ngày tải lên: 24/12/2013, 12:16

... has an error term; but we neglected the fact that the LU decomposition of A is itself not exact. A different analytical approach starts with some matrix B 0 that is assumed to be an approximate ... (North America only),or send email to trade@cup.cam.ac.uk (outside North America). We can define the norm of a matrix as the largest amplification of length that it is able to induce on a ve...

Ngày tải lên: 24/12/2013, 12:16

... distinct (and not always compatible) goals for any sparse matrix method: saving time and/or saving space. We have already considered one archetypal sparse form in §2.4, the band diagonal matrix. ... pythag(float a, float b) Computes (a 2 + b 2 ) 1/2 without destructive underflow or overflow. { float absa,absb; absa=fabs (a) ; absb=fabs(b); if (absa > absb) return absa*sqrt(1.0+SQR(absb/abs...

Ngày tải lên: 24/12/2013, 12:16