Tài liệu Solution of Linear Algebraic Equations part 6 pptx

... 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,Numerical Methods(Englewood Cliffs, NJ: Prentice-Hall),§5.5 .6, p. 183.Forsythe, G.E., and Moler, C.B. 1 967 ,Computer Solution of Linear Algebraic Systems(Engle-wood Cliffs, NJ: Prentice-Hall),...

Tài liệu Solution of Linear Algebraic Equations part 1 docx

... trade@cup.cam.ac.uk (outside North America).Chapter 2. Solution of Linear Algebraic Equations 2.0 IntroductionA set of linear algebraic equations looks like this:a11x1+ a12x2+ a13x3+ ... equations as unknowns, and there is a goodchance of solving for a unique solution set of xj’s. Analytically, there can fail tobe a unique solution if one or more of the M equations is a linear ... can be either no solution, or else more than one solution vector x. In the latter event, the solution space consists of a particular solution xpadded to any linear combination of (typically)...

Tài liệu Solution of Linear Algebraic Equations part 2 ppt

... case of N × N matrices, with M sets of right-handside vectors, in completely analogous fashion. The routine implemented belowis, of course, general.38Chapter 2. Solution of Linear Algebraic Equations Sample ... G.E., and Moler, C.B. 1 967 ,Computer Solution of Linear Algebraic Systems(Engle-wood Cliffs, NJ: Prentice-Hall).Wilkinson, J.H., and Reinsch, C. 1971, Linear Algebra,vol.IIofHandbook for Automatic ... 36 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...

Tài liệu Solution of Linear Algebraic Equations part 11 ppt

... 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.98Chapter 2. Solution of Linear Algebraic Equations Sample ... not used for typical systems of linear equations. However, we willmeet special cases where QR is the method of choice.100Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... America).x[i]=sum/p[i];}}A typicaluseof choldcand cholslis in theinversionof covariancematrices describingthe ﬁt of data to a model; see, e.g., §15 .6. In this, and many other applications,one often needsL−1....

Tài liệu Solution of Linear Algebraic Equations part 3 pdf

... 42Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... Sciences(New York:McGraw-Hill), Program B-2, p. 298.Westlake, J.R. 1 968 ,A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley).Ralston, A., and Rabinowitz, P. 1978,A ... 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...

Tài liệu Solution of Linear Algebraic Equations part 4 docx

... 1 967 ,Computer Solution of Linear Algebraic Systems(Engle-wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.Westlake, J.R. 1 968 ,A Handbook of Numerical Matrix Inversion and Solution of ... (i=j;i<=n;i++) { This is i = j of equation (2.3.12) and i = j +1 N of equation (2.3.13).sum=a[i][j];for (k=1;k<j;k++)44Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... (i.e., selection of a salubrious pivot elementfor the division in equation 2.3.13) is absolutely essential for the stability of Crout’s50Chapter 2. Solution of Linear Algebraic Equations Sample...

Tài liệu Solution of Linear Algebraic Equations part 5 docx

... 1 967 ,Computer Solution of Linear Algebraic Systems(Engle-wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.Westlake, J.R. 1 968 ,A Handbook of Numerical Matrix Inversion and Solution of ... (j=LMAX(1,1-k);j<=tmploop;j++) b[i] += a[i][j]*x[j+k];}}54Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... Chapter I /6. [1]Golub, G.H., and Van Loan, C.F. 1989,Matrix Computations, 2nd ed. (Baltimore: Johns HopkinsUniversity Press),§4.3.50Chapter 2. Solution of Linear Algebraic Equations Sample...

Tài liệu Solution of Linear Algebraic Equations part 12 pdf

... 104Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... R1× a12R4= a21× R3R5= R4− a22R 6 = Inverse(R5)c12= R3× R 6 c21= R 6 × R2R7= R3× c21c11= R1− R7c22= −R 6 (2.11 .6) ... divisions inall! So divisions don’t dominate in the recursive use of (2.11 .6) . Equation (2.11 .6) is dominated, in fact, by its 6 multiplications. Since these can be done by an Nlog27algorithm,...

Tài liệu Solution of Linear Algebraic Equations part 7 docx

... x = bSVD solution  of A ⋅ x = csolutions of A ⋅ x = c′solutions of A ⋅ x = dnullspace of ASVD solution of A ⋅ x = drange of Adc(b)(a)Axbc′Figure 2 .6. 1. (a) A ... b=0, q.e.d.Figure 2 .6. 1 summarizes our discussion of SVD thus far. 68 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... N(2 .6. 2)Nj=1VjkVjn= δkn1 ≤ k ≤ N1 ≤ n ≤ N(2 .6. 3) 66 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...

Tài liệu Solution of Linear Algebraic Equations part 8 docx

... case of a tridiagonal matrix was treated specially, because thatparticular type of linear system admits a solution in only of order N operations,rather than of order N3for the general linear ... Package [6] .You should be aware that the special order of interchanges and eliminations,84Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... residualr1= b − A · x1(2.7. 36) and chooser1= r1. Then form the sequence of improved estimatesxk+1= xk+ αkpk(2.7.37) 76 Chapter 2. Solution of Linear Algebraic Equations Sample page from...

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