Elementary linear algebra

... otherwise stated, the field used will be Q. 6 CHAPTER 1. LINEAR EQUATIONS 1.2 Solving linear equations We show how to solve any system of linear equations over an arbitrary field, using the GAUSS–JORDAN ... operations are the ones used on systems of linear equations and do not change the solutions. DEFINITION 1.2.3 (Elementary row operations) There are three types of elementary row o...

Ngày tải lên: 31/03/2014, 15:02

... 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 + ... wrong: • While not exact linear combinations of each other, some of the equations may be so close to linearly dependent that roundoff errors in the machine render them linearly dependent...

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 ... 36 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... is the identity matrix, simultaneously solves the linear se...

Ngày tải lên: 15/12/2013, 04:15

... 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 ... 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. 100 Chapter 2. Solution of Linear...

Ngày tải lên: 15/12/2013, 04:15

... Exercises Linear Algebra Jim Hefferon  2 1   1 3      1 2 3 1      2 1  x 1 ·  1 3      x · 1 2 x · 3 1      2 1   6 8      6 2 8 1     8 Linear Algebra, by ... straightforward cancelling on both sides of the i-th equation), which says that (s 1 , . . . , s n ) 10 Linear Algebra, by Hefferon solves a 1,1 x 1 + a 1,2 x 2 + ··· + a 1,n x n = d 1 . ....

Ngày tải lên: 15/12/2013, 21:17

... this point. The procedure up to this point is termed Gaussian elimination. 42 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... Program B-2, p. 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 Cours...

Ngày tải lên: 24/12/2013, 12:16

... solve the linear set A · x =(L·U)·x=L·(U·x)=b (2.3.3) by first solving for the vector y such that L · y = b (2.3.4) and then solving U · x = y (2.3.5) What is the advantage of breaking up one linear ... (2.2.2)– (2.2.4), x N = y N β NN x i = 1 β ii   y i − N  j=i+1 β ij x j   i = N − 1,N −2, ,1 (2.3.7) 44 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL R...

Ngày tải lên: 24/12/2013, 12:16

... 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 ... 50 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... course, this is only a useful classification if m 1 an...

Ngày tải lên: 24/12/2013, 12:16

... 102 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... updating, in §9.7. CITED REFERENCES AND FURTHER READING: Wilkinson, J.H., and Reinsch, C. 1971, Linear Algebra ,vol.IIof Handbook for Automatic Com- putation (New York: Springer-Verlag), Chapter

Ngày tải lên: 24/12/2013, 12:16