solution of linear equations using gaussian elimination
Tài liệu Solution of Linear Algebraic Equations part 1 docx
... IntroductionA set of linear algebraic equations looks like this:a 11 x 1 + a 12 x2+ a 13 x3+ ···+a1NxN=b 1 a 21 x 1 + a22x2+ a23x3+ ···+a2NxN=b2a 31 x 1 + a32x2+ a33x3+ ···+a3NxN=b3··· ... 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 Algebraic Equations 2.0 IntroductionA set of linear algebraic ... section 34Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... equationa11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44·x11x 21 x31x41x 12 x 22 x 32 x 42 x13x 23 x33x43y11y 12 y13y14y 21 y 22 y 23 y 24 y31y 32 y33y34y41y 42 y43y44=b11b 21 b31b41b 12 b 22 b 32 b 42 b13b 23 b33b431000010000100001 (2. 1.1)Here ... equationa11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44·x11x 21 x31x41x 12 x 22 x 32 x 42 x13x 23 x33x43y11y 12 y13y14y 21 y 22 y 23 y 24 y31y 32 y33y34y41y 42 y43y44=b11b 21 b31b41b 12 b 22 b 32 b 42 b13b 23 b33b431000010000100001 (2. 1.1)Here ... 36Chapter 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) 1988-19 92 by Cambridge University...
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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 ... matrixmultiplication of two 2 ì 2 matrices,a 11 a12a21a22Ãb 11 b12b21b22=c 11 c12c21c22(2 .11. 1)Eight, right? Here they are written explicitly:c 11 = a 11 ì b 11 + a12ì b21c12=...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... case of a single right-hand side vector):a11a12a 13 a140 a22a 23 a2400a 33 a 34 000a44·x1x2x 3 x4=b1b2b 3 b4(2.2.1)Here ... identitymatrix),Gaussianeliminationandbacksubstitutionatfirstglancerequire1 3 N 3 (matrixreduction) +12N 3 (right-hand side manipulations) +12N 3 (N backsubstitutions)=4 3 N 3 loop executions, which is more than the N 3 for Gauss-Jordan. ... 42Chapter 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) 1988-1992 by...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
... β22β23β 24 00β33β 34 000β 44 =a11a12a13a 14 a21a22a23a 24 a31a32a33a 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 setA ... case of a 4 ì 4 matrix A, for example, equation (2.3.1) would look like this:α11000α21α2200α31α32α330α 41 α 42 α 43 α 44 ·β11β12β13β 14 0 β22β23β 24 00β33β 34 000β 44 =a11a12a13a 14 a21a22a23a 24 a31a32a33a 34 a 41 a 42 a 43 a 44 (2.3.2)We ... brief,Crout’s method fills in the combined matrix of α’s and β’s,β11β12β13β 14 α21β22β23β 24 α31α32β33β 34 α 41 α 42 α 43 β 44 (2.3. 14) by columns from left to right, and within...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
... 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 SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright (C) 1988-1992 ... HopkinsUniversity Press),Đ4.3. 50 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...
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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 ... submatrices. Imagine doing the inversionof a very large matrix, of orderN =2m, recursively by partitions in half. At each step, halving the order doublesthe number of inverse operations. But this ... matricesa11a 12 a21a22andc11c 12 c21c22(2.11.5)are inverses of each other. Then the c’s can be obtained from the a’s by the followingoperations (compare equations 2.7.22...
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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),Đ5.5 .6, p. 183.Forsythe, G.E., and Moler, C.B. 1 967 ,Computer Solution of Linear Algebraic Systems(Engle-wood Cliffs, NJ: Prentice-Hall),...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
... makingthe same permutation of the columns of U,elementsofW,andcolumnsofV(orrows of VT), or (ii) forming linear combinations of any columns of U and V whosecorresponding 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 = bSVD solution of A ⋅ x = csolutions of A ⋅ x = c′solutions of A ⋅ ... space into one of lower dimensionality, here a plane into a line, called the “range” of A.The“nullspace” of A is mappedto zero. The solutions of A · x = d consist of any one particular solution plusany...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
... 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 08- 5)Copyright (C) 1 988 -1992 by Cambridge ... omitted rows. 78 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...
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Tài liệu Solution of Linear Algebraic Equations part 9 docx
... 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) 198 8- 199 2 by Cambridge ... precision. 94 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 University...
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Tài liệu Solution of Linear Algebraic Equations part 10 docx
... 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, 98Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 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...
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Tài liệu Báo cáo " Fully parallel methods for a class of linear partial differential-algebraic equations " pptx
... 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 Linear Parabolic Problems, Applied Mathematics ... parallel methods for solving linear partial differential-algebraic equations (PDAEs) of the form:Aut+ B∆u = f(x, t) (1)where A is a singular, symmetric and nonnegative matrix, while B is a...
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Tài liệu Đề tài " Isomonodromy transformations of linear systems of difference equations" pptx
... ,k2s∈{0, 1, ,N}; this Annals of Mathematics Isomonodromy transformations of linear systems of difference equations By Alexei Borodin ISOMONODROMY TRANSFORMATIONS 1147probability ... a polynomial of degree n −1.Lemma 3.2. A linear function z −B is a right divisor of A(z) if and onlyifA0Bn+ A1Bn−1+ ···+ An=0.Proof. See, e.g., [GLR]. ISOMONODROMY TRANSFORMATIONS 1169Thus, ... solutions of isomonodromy problems for such systems of difference equations. In the case of one-interval gap probability this has been done (in a different language) in[Bor], [BB]. One example of the...
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solution of linear equations using gaussian elimination
... ObjectivesIntroduction Gaussian elimination method Gaussian elimination procedureProgramming exerciseGeneral informationTitle: Solution of linear equations using Gaussian elimination Teacher(s): Professor ... Solution of linear equations using Gaussian elimination FAQReferencesSummaryInfoResourcesLearning ObjectivesIntroduction Gaussian elimination method Gaussian elimination procedureProgramming ... NAG-libraryFAQReferencesSummaryInfoResourcesLearning ObjectivesIntroduction Gaussian elimination method Gaussian elimination procedureProgramming exerciseIntroduction Solution of sets of linear equations is required in many petroleum...
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