chapter 2 solution of linear algebraic equations
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 ... 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 (C) 1988-19 92 by Cambridge...
- 6
- 410
- 0
Tài liệu Solution of Linear Algebraic Equations part 1 docx
... 1-800-8 72- 7 423 (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 equations ... this:a11x1+ a 12 x 2 + a13x3+ ···+a1NxN=b1a 21 x1+ a 22 x 2 + a 23 x3+ ···+a2NxN=b 2 a31x1+ a 32 x 2 + a33x3+ ···+a3NxN=b3··· ···aM1x1+aM2x 2 +aM3x3+···+aMNxN= ... improvement of a solution ( 2. 5)ã Various special forms: symmetric positive-denite ( 2. 9), tridiagonal( 2. 4), band diagonal ( 2. 4), Toeplitz ( 2. 8), Vandermonde ( 2. 8), sparse( 2. 7)ã Strassens...
- 5
- 461
- 0
Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... matrices,a11a 12 a 21 a 22 Ãb11b 12 b 21 b 22 =c11c 12 c 21 c 22 (2. 11.1)Eight, right? Here they are written explicitly:c11= a11ì b11+ a 12 ì b 21 c 12 = a11ì b 12 + a 12 ì b 22 c 21 = a 21 ì ... set of formulas was, in fact, discovered by Strassen[1]. The formulas are:Q1 (a11+ a 22 ) ì (b11+ b 22 )Q 2 (a 21 + a 22 ) ì b11Q3 a11ì (b 12 b 22 )Q4 a 22 ì (b11+ b 21 )Q5 ... b11+ a 12 ì b 21 c 12 = a11ì b 12 + a 12 ì b 22 c 21 = a 21 ì b11+ a 22 ì b 21 c 22 = a 21 ì b 12 + a 22 ì b 22 (2. 11 .2) Do you think that one can write formulas for the c’s that involve only...
- 5
- 357
- 0
Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... 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) 1988-19 92 by Cambridge ... isxi=1aiibi−Nj=i+1aijxj (2. 2.4)The procedure defined by equation (2. 2.4) is called backsubstitution.Thecom-bination of Gaussian elimination and backsubstitution yields a solution to the set of equations. The ... the case of a single right-hand side vector):a11a 12 a13a140 a 22 a 23 a 24 00a33a34000a44·x1x 2 x3x4=b1b 2 b3b4 (2. 2.1)Here...
- 3
- 404
- 0
Tài liệu Solution of Linear Algebraic Equations part 4 docx
... β 22 β 23 β 24 00β33β34000β44=a11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44 (2. 3 .2) We can use a decomposition such as (2. 3.1) to solve the linear setA · x =(L·U)·x=L·(U·x)=b (2. 3.3)by ... j : αi1β1j+ αi2β2j+ ···+αiiβjj= aij (2. 3.9)i>j: αi1β1j+αi2β2j+···+αijβjj= aij (2. 3.10) Equations (2. 3.8)– (2. 3.10) total N 2 equations for the N 2 + N unknown α’s ... case of a 4 ì 4 matrix A, for example, equation (2. 3.1) would look like this:α11000α 21 α 22 00α31α 32 α330α41α 42 α43α44·β11β 12 β13β140 β 22 β 23 β 24 00β33β34000β44=a11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44 (2. 3 .2) We...
- 8
- 464
- 0
Tài liệu Solution of Linear Algebraic Equations part 5 docx
... elimination.dum=a[i][1]/a[k][1];al[k][i-k]=dum;for (j =2; j<=mm;j++) 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 ... 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 ... Computations, 2nd ed. (Baltimore: Johns HopkinsUniversity Press),Đ4.3. 50 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
- 6
- 426
- 0
Tài liệu Solution of Linear Algebraic Equations part 12 pdf
... Inverse(a11)R 2 = a 21 ì R1R3= R1ì a 12 R4= a 21 ì R3R5= R4 a 22 R6= Inverse(R5)c 12 = R3ì R6c 21 = R6ì R 2 R7= R3ì c 21 c11= R1 R7c 22 = R6 (2. 11.6) ... matricesa11a 12 a 21 a 22 andc11c 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 followingoperations (compare equations 2. 7 .22 and 2. 7 .25 ):R1= Inverse(a11)R 2 = a 21 ì R1R3= ... 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) 1988-19 92 by Cambridge...
- 3
- 312
- 0
Tài liệu Solution of Linear Algebraic Equations part 6 pptx
... 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 (C) 1988-19 92 by Cambridge ... quite far from the true solution, one call is generally enough; but a secondcall to verify convergence can be reassuring. 58 Chapter 2. Solution of Linear Algebraic Equations Sample page from ... feasible)? 2. 5 Iterative Improvement of a Solution to Linear Equations 55Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge...
- 5
- 369
- 0
Tài liệu Solution of Linear Algebraic Equations part 7 docx
... (scale) { 62 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) 1988-19 92 by Cambridge ... 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 (ISBN 0- 521 -43108-5)Copyright ... 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 (C) 1988-19 92 by Cambridge...
- 13
- 383
- 0
Tài liệu Solution of Linear Algebraic Equations part 8 docx
... 0. 0. 0. 2. 0. 0. 0. 6. 5. (2. 7 .27 ) 74 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 ... 1978(Philadelphia:S.I.A.M.). 82 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) 1988-19 92 by Cambridge ... j,jl,jm,jp,ju,k,m,n2,noff,inc,iv;float v;n2=ija[1]; Linear size of matrix plus 2. for (j=1;j<=n2 -2; j++) sb[j]=sa[j]; Diagonal elements.iindexx(ija[n2-1]-ija[1],(long *)&ija[n2-1],&ijb[n2-1]);Index...
- 20
- 410
- 0
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) 1988-19 92 by Cambridge ... equations 11··· 1x1x 2 ··· xNx 2 1x 2 2··· x 2 N···xN−11xN−1 2 ··· xN−1N·w1w 2 w3···wN=q1q 2 q3···qN (2. 8 .2) Write this ... xj.Inotherwords,Pj(xi)=δij=Nk=1Ajkxk−1i (2. 8.4)But (2. 8.4) saysthat Ajkis exactly the inverse of the matrix of componentsxk−1i,whichappears in (2. 8 .2) , with the subscript as the column index. Therefore the solution of (2. 8 .2) is...
- 7
- 389
- 0
Tài liệu Solution of Linear Algebraic Equations part 10 docx
... +1,i +2, ,N (2. 9.5) 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) 1988-19 92 by ... byLTij= Lji (2. 9.3)Writing out equation (2. 9 .2) in components, one readily obtains the analogs of equations (2. 3. 12) – (2. 3.13),Lii=aii−i−1k=1L 2 ik1 /2 (2. 9.4)andLji=1Liiaij−i−1k=1LikLjkj ... 96 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) 1988-19 92 by Cambridge...
- 10
- 350
- 0
Tài liệu Chapter 2: Indicators of Financial Structure, Development, and Soundness ppt
... of the outreach of bank-ing outlets. 25 Chapter 2: Indicators of Financial Structure, Development, and Soundness1IHGFEDCBA 12 11109876543 2 distribution of stress tests results, ... other indicators of competition. See chapter 4 for a discussion of model-based indicators of competition.6. For an example of the computation of the Herfindahl index, see chapter 15 of the Compilation ... discussion of these indicators can be found in section 2. 2.4.Table 2. 2 summarizes the indicators of financial system performance that have been discussed in this section. 2. 1.4 Scope and Coverage of...
- 19
- 543
- 0
Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
... Đ1.8 Chapter 2 Chapter 3 Chapter 5Đ6.1 Đ6 .2 Đ6.3Đ7.1 Đ7 .2 Đ7.3 Đ7.4Đ8.1 Đ8 .2 Đ8.3 Đ8.4 Đ8.5 Đ8.6 Đ8.8 Chapter 9 Chapter 10 Chapter 11Đ 12. 1 Đ 12. 2Đ13.1 Đ13 .2 Đ13.3 Đ13.4 Đ13.7 Chapter ... proofs the selected material provides the underlying mathe-matics. Chapter 1 Chapter 2 Chapter 4 Chapter 5Đ6.1 Đ6 .2 Đ6.3Đ7.1 Đ7 .2 Đ7.3 Đ7.4Đ8.1 Đ8 .2 Đ8.3 Đ8.4 Đ8.5 Đ8.6 Đ8.8 Đ8.9 Chapter ... background:Đ1.1 Đ1 .2 Đ1.3 Đ1.4 Đ1.5 Đ1.6 Đ1.7 Đ1.8Đ5.1 Đ5 .2 Đ5.3 Đ5.4Đ6.1 Đ6 .2 Đ6.3Đ7.1 Đ7 .2 Đ7.3 Đ7.4Đ8.1 Đ8 .2 Đ8.3 Đ8.4 Đ8.5 Đ8.6 Đ8.8Đ11.1 Đ11 .2 Đ11.3 Đ11.4 Đ11.5Đ 12. 1 Đ 12. 2Đ13.1 Đ13 .2 Đ13.3...
- 868
- 1,280
- 0
Chapter 2 Flow of Control potx
... Copyright â 20 06 Pearson Addison-Wesley. All rights reserved. 2- 9Display 2. 3 Precedence of Operators (4 of 4) Copyright â 20 06 Pearson Addison-Wesley. All rights reserved. 2- 5Evaluating ... Display 2. 2 Truth Tables Copyright â 20 06 Pearson Addison-Wesley. All rights reserved. 2- 33Comma OperatorEvaluate list of expressions, returningvalue of the last expression♦Most often ... Addison-Wesley. All rights reserved. 2- 8Display 2. 3 Precedence of Operators (3 of 4) Copyright â 20 06 Pearson Addison-Wesley. All rights reserved. 2- 12 if-else Statement Syntax♦Formal syntax:if...
- 42
- 441
- 0
Tìm thêm: xác định các mục tiêu của chương trình xác định thời lượng học về mặt lí thuyết và thực tế tiến hành xây dựng chương trình đào tạo dành cho đối tượng không chuyên ngữ tại việt nam điều tra đối với đối tượng giảng viên và đối tượng quản lí điều tra với đối tượng sinh viên học tiếng nhật không chuyên ngữ1 khảo sát thực tế giảng dạy tiếng nhật không chuyên ngữ tại việt nam khảo sát các chương trình đào tạo theo những bộ giáo trình tiêu biểu nội dung cụ thể cho từng kĩ năng ở từng cấp độ xác định mức độ đáp ứng về văn hoá và chuyên môn trong ct mở máy động cơ lồng sóc mở máy động cơ rôto dây quấn các đặc tính của động cơ điện không đồng bộ đặc tuyến hiệu suất h fi p2 đặc tuyến mômen quay m fi p2 đặc tuyến tốc độ rôto n fi p2 sự cần thiết phải đầu tư xây dựng nhà máy thông tin liên lạc và các dịch vụ phần 3 giới thiệu nguyên liệu chỉ tiêu chất lượng theo chất lượng phẩm chất sản phẩm khô từ gạo của bộ y tế năm 2008 chỉ tiêu chất lượng 9 tr 25