chapter 2 solution of linear algebraic equations

... −1  (2.7.12) 76 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) 1988-1992 by Cambridge ... equation (2.7.24) and (2.7.25) depends on whether you want  P or  S to have the 78 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... right-hand side to 72 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) 1988-1992 by Cambridge

Ngày tải lên: 24/12/2013, 12:16

... invariants 3.4.2 Over determined systems 23 23 23 23 24 24 26 27 27 27 29 29 30 31 31 31 Chapter BDF-methods 4.1 Multi Step-Methods in general and BDF-methods 4.1.1 BDF-methods 4.2 BDF-methods ... order, stiff accuracy 2.1.4 Collocation methods 2.2 Runge-Kutta Methods for Problems of Index 2.2.1 State Space Form Method 2.2.2 The ε-embedding method for problems of index 2.3 Runge-Kutta Methods ... Computation of Impasse Points of Quasi-Linear Differential-Algebraic Equations Math Comp., 62(205):133–154, January 1994 [PR94b] W.C Rheinboldt P.J Rabier On the Computation of Impasse Points of Quasi-Linear

Ngày tải lên: 21/12/2016, 10:52

... Trang 12 Solution of non-linear algebraic equations 2.1 Introduction In the solution of linear problems by a finite element method we always need to solve a set of simultaneous algebraic equations ... * l - 1 d(a')TqL-' (2.23) 1 & - I w, = Y where y is defined by Eq (2.21) Some algebra will readily verify that substitution of Eqs (2.22) and (2.23) into Eq (2.21) results in an identity ... other special examples 2.2 Iterative techniques 2.2.1 General remarks The solution of the problem posed by Eqs (2.3)-(2.6) cannot be approached directly and some form of iteration will always

Ngày tải lên: 02/05/2018, 13:39

... 1M2q − m p 1m q2 p M1m2M2q − m1M2m q2 1/p q m1M2M p1− M1m2m p1 1/q . 2.7 Note that if m1  0, m2/  0 or m2  0, m1/ 0, obviously, 2.6 holds If m1  m2  0, choose c p,q ∞, then 2.6 ... Remark 2.5 If p  q  2, then we obtain Cauchy-Schwarz inequality: n  k1 a k b k≤ n k1 a2k 1/2n k1 b2k 1/2 ≤ c2 n  k1 a k b k , 2.8 where c2 ⎛ ⎝ M1M2 m1m2   m1m2 M1M2 ⎞ Remark 2.6 ... m1/M1p m q2 M 1/p1 p m2M2q −m1/M1M2m q2 1/p M q/p1  q m1M2−M1m2m1/M1p1/q  limp → ∞ q → 1 M2 M 1/pp/q−p1 m1M2  limp → ∞ q → 1 1 M 1/p−11 m1  M1 m1. 2.10 Let p → ∞, q → 1 in 2.6, then

Ngày tải lên: 22/06/2014, 03:20

... 11 x 1 + a 12 x 2 + a 13 x 3 = d 1 a 21 x 1 + a 22 x 2 + a 23 x 3 = d 2 a 31 x 1 + a 32 x 2 + a 33 x 3 = d 3 (4) (5) (6) ′ a 22 x 2 + ′ a 23 x 3 = ′ d 2 ′ a 32 x 2 + ′ a 33 ... 1 + a 12 x 2 + a 13 x 3 = d 1 ′ a 22 x 2 + ′ a 23 x 3 = ′ d 2 ′ a 32 x 2 + ′ a 33 x 3 = ′ d 3 (7) (8) (9) a 11 x 1 + a 12 x 2 + a 13 x 3 = d 1 ′ a 22 x 2 + ′ a 23 x 3 ... concept of simultaneous linear equations. A set of linear simultaneous equations may be written as: a 11 x 1 +a 12 x 2 + a 13 x 3 + + a 1N x N = d 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + + a 2N x

Ngày tải lên: 24/10/2014, 21:28

... s2,…, sn is called a solution to a system of linear equations if s1,s2,…,sn is a solution to every equation of the system ⚫ A system may have no solution, may have unique solution (nghiệm duy ... Engineering ⚫ a1x1+a2x2+…+anxn=b is called a linear equation ( phương trình tuyến tính ) ⚫ A solution ( nghiệm) to the equation is a sequence s1, s2,…, snsuch that a1s1+a2s2+…+ansn=b ⚫ s1, s2,…, sn is ... duytq4@fpt.edu.vnChapter 1 Systems of Linear Equations Trang 2Dr Tran Quoc Duy Mathematics for Engineering Contents 1 Solutions and Elementary Operations 2 Gaussian Elimination 3 Homogeneous Equations

Ngày tải lên: 27/10/2019, 22:52

... ( 2(A+1) 5 2 G(Q)= | M2 AT AI? |, 0 N24+BAF2 With the maximum norm of R?, ie., ||(a, y)|| = max{|a|, |y|} we have |A2+3A+2||A2+3A+2|J |A2+3A+2| |GO)|| = max { =ms*parn) — |A+2| |A+1|2 Put ... < Nia leg (t,7) + 3N7ag|(t— T)e_ 20 (4,7) Further, from the relation (—¥)6(—$)(t) = —22+(—22)? u(t) > —22, it follows that e_a(t,7).e_a(t,7) = e(-a)@(-2)(47 7) > €_z.(, 7) On the other ... extendibility of solution of initial value problem (7) we can refer to [15] On exponential stability of dynamic equations on time scales, we often use one of two following definitions Let w(t) = a(t,7, 20)

Ngày tải lên: 22/03/2014, 11:20

... Trang 1Chapter 2: Selection of Independent Auditors 2.1 This chapter provides guidance to recipients in selecting independent auditors ... reduced audit costs Chapter 8 of these Guidelines presents an outline of an illustrative statement of work to be included in recipient-contracted audit agreements Audit Firms 2.5 The OIG must ... auditing guidelines of the International Auditing Practices Committee of the International Federation of Accountants (IFAC) e Maintains a continuing program of staff training and professional development

Ngày tải lên: 19/06/2014, 21:20

... Consideration of the Internal Audit Function in an Audit of Financial Statements 322 70 Reports on the Processing of Transactions by Service Organizations 324 71 Interim Financial Information 722 ... Pittsburgh, PA 15250-7954, or by telephone The order desk telephone number is (202) 512-1800 or 866 512-1800-4.29 Office of Management and Budget (OMB) Circulars The following circulars can be obtained ... Items of a Financial Statements 622 77 Amendments to SAS No 22, Planning and Supervision, No 59, The Auditor's Consideration of an Entity's Ability to Continue as a Going Concern, and No 62,

Ngày tải lên: 19/06/2014, 21:20

... Audits of Awards with Annual Cost-Sharing Budgets FROM JANUARY 1, 20XX TO DECEMBER 31, 20XX 22 CASH Grant No 1 Grant No 2 $xxx xxx $xxx xxx $xxx $xxx Note 1 IN-KIND Grant No 1 Grant No 2 ... of computation of indirect cost rate (see Example 6.3 of these Guidelines) and the auditor's report on the schedule of computation of indirect cost rate This should be a Revised on January 2006 ... January 2006 43 This is trial version www.adultpdf.com Trang 10Example 6.3 - Illustrative Schedule of Computation of Indirect Cost Rate (NAME OF RECIPIENT) SCHEDULE OF COMPUTATION OF INDIRECT

Ngày tải lên: 19/06/2014, 21:20

... Board of Directors Name of Recipient Organization Complete Mailing Address We have audited the fund accountability statement of (name of recipient) as of and for the year ended June 30, 20XX, ... statement of (name of recipient) for the year ended June 30, 20XX, we obtained an understanding of internal control With respect to internal control, we obtained an understanding of the design of relevant ... statement of (name of recipient) for the year ended June 30, 20XX, we obtained an understanding of internal control With respect to internal control, we obtained an understanding of the design of relevant

Ngày tải lên: 19/06/2014, 21:20

... 8.09-0 042 Washington, DC 20523-8100 N/A TEL: 202-712-5480/1326 1150/1170 FAX: 202-216-3598 3801 *Inspector General Hotline for Reporting Fraud, Waste and Abuse Telephones:45 1-800-230-6539 ... reviewed the accompanying schedule of counterpart contributions of (name of recipient) for the period (date of beginning of current audit period) to (date of end of current audit period) Our review ... (QCRs) of the workpapers of a sample of audit reports The OIG will notify the auditee of the results of the QCRs If the OIG does not accept an audit report because of deficiencies in the work of

Ngày tải lên: 19/06/2014, 21:20

... FY2006 FY2007 FY2008 FY2009 FY2010 TAX 107 Supporting Services – Revenue Collection $452,000 $452,000 $452,000 $869,000 $452,000 Total Department Appropriations $22,126,013 $22,288,039 $25,805,566 ... Appropriations General Funds FY2006 FY2007 FY2008 FY2009 FY2010 TAX 102 Income Assessment and Audit $4,727,884 $4,757,096 $0 $0 $0 TAX 103 Tax Collections Enforcement $3,440,558 $3,628,186 $0 $0 $0 TAX ... Appropriations $22,126,013 $22,288,039 $25,805,566 $24,941,043 $22,628,219 Source: General and Supplemental Appropriations Act. FY2008 - TAX 102 and TAX 103 were consolidated into a new program

Ngày tải lên: 20/06/2014, 02:20

... monitoring of vendor work hours for the 2009 modication was inadequate. Exhibit 2.1 summarizes the department’s follow through with 2008 contract and 2009 modication requirements. Exhibit 2.1 Summary ... compiled by Ofce of the Auditor This is trial version www.adultpdf.com 19 Chapter 2: Lack of Planning and Fractured Management Undermine the State’s Tax Collection Efforts According to the 2008 contract, ... discontinued within a year of the signing of the 2008 contract. The committee maintained an open and closed log to record its discussions—the last entry was on October 8, 2008. The 2009 modication also

Ngày tải lên: 20/06/2014, 02:20

... reviewed the 2008 contract and noted that the majority of its 22 initiatives—as shown in Exhibit 2.2—do not involve the assessment, enforcement, or collection of taxes as required by Section 231-13, ... $9.8 million The 2009 contract modification removed the obligation of the vendor to complete the 2008 contract’s 22 initiatives Instead, the modification included a list of 21 revenue generating ... State of about $24.4 million The additional revenue generated from this program would have been deposited to the State’s general fund Exhibit 2.2 2008 Contract Initiatives 2 Integration of Miscellaneous

Ngày tải lên: 20/06/2014, 02:20

... 2002 2003 2004 2005 2006 2007 2008 2009 2010 13 15 16 16 19 24 25 23 21 21 21 20 Source: Office of the Auditor based on data provided by the Department of Taxation and the department’s ITS Office ... Exhibit 2.3 shows the number of ITS Office staff over the past 12 years from 1999 to present Exhibit 2.3 ITS Office Staffing Levels Number of ITS Office Staff from 1999 – 2010 1999 2000 2001 2002 2003 ... several had balance differences of several hundreds of thousands of dollars, with the highest difference being in excess of $4.3 million As of July 2010, there were 241,753 existing transaction

Ngày tải lên: 20/06/2014, 02:20

...  (k + 1)!2 (2k + 2)! 2k + 1 k + 1 = (k!) 2 2(2k)!,  (k + 1)!2 (2k + 2)! k + 1 k =  (k −1)! 2 4 4− k −2  (2k −2)!. (3.8) Thus, relation (3.7) becomes σk+1(z) = z + 1 2 (k!)2 (2k)!(z −1)k ... -Ak1 ,k2-stable if C− ⊆Ᏸk1k2, where Ᏸk1k2=q ∈ C:π(z,q) is of typek1, 0,k2  (2.7) denotes the region of ( k1,k2)-Absolute stability; - Perfectly Ak1 ,k2-stable if C− ≡Ᏸk1k2. Remark 2.3 The ... z + 1 Proof From (3.2) one has σk+1(z) =[(k + 1)!]2 (2k + 2)! (z −1)k+1 Lk+1 z + 1 z −1  By using (3.3) in the previous relation we get σk+1(z) =  (k + 1)!2 (2k + 2)! (z −1)k+1 2k + 1 k

Ngày tải lên: 23/06/2014, 00:20

... 3.2 implementation  208 3.2.1 an introduction to RDEAM  209 3.2.2 interpolation formulae  214 3.2.3 stcpsize modifications  218 3.2.4 error estimation, stcpsize and order control  222 ... discontinuities  65 2.1.4 accuracy  74 2.2 linear multistep and predictor corrector methods  75 2.2.1  linear multistep formulae  76 2.2.2 predictor-corrector methods  79 2.3 stability  84 2.4 stepsize ... error control  117 2.6.1 ordinary differential equations  118 2.6.2 systems of equations  136 2.6.3 delay-equations  137 2.7 detecting derivative discontinuities  152 4 Chapter three - DELSOL

Ngày tải lên: 11/10/2014, 04:02

... The Numerical Solution of Delay-differential Equations by David Richard Wile Department of Mathematics University of Manchester volume II of II A thesis submitted to the University of Manchester ... degree of Doctor of Philosophy in the Faculty of Science. October 1989 290 0 Contents • Volume Two - title page  289 - contents page for volume two  290 Appendicies A  a formal proof for ... example.  407 D  -  a listing of the root location algorithm discussed in (2.7)  415 Bibliography  418 291 appendix A a formal proof for (1.1.3:14) 292 A formal proof for (1.1.3:14) In this appendix

Ngày tải lên: 11/10/2014, 04:03

... States (20 02) : pp 27 2 -28 6 [2] Ferguson, Renee Boucher, “E-Sourcing Apps Lead to Time Well-Spent,” eWeek, © Copyright 20 03 Ziff Davis Media Inc., Ziff Davis Media Inc 28 East 28 th Street, ... (box B in Figure 2. 2), using different B2B protocols... Finally, the last part of this chapter discusses connectivity, how to use a B2B protocol exchange, and how many of these protocols ... enjoyed by purchasers of legitimate software, such as customer support and product upgrades. But, the economic impact of software piracy extends far beyond the confines of the software industry and

Ngày tải lên: 13/11/2014, 12:59