numerical solutions of nonlinear algebraic equations by secant bisection and newtonraphson methods
Numerical Solutions of the Black Scholes Equation
... 8 Numerical Solutions of the BlackScholes Equation8.1 FINITE DIFFERENCE APPROXIMATIONS(i) The object of this chapter is to explain various methods of solving the Black Scholes equation by numerical ... the left-handedge of the grid (initial conditions) and the values atthe top and bottom edges (boundary conditions); thesolution of the problem is the series of values at theright-hand edge. ... Solution of implicit methodi.e. we know uiM and ui−M. We can therefore calculate the right-hand side of equation (8.4)since we also know the elements of the matrix B; this will be designated by...
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Tài liệu Solution of Linear Algebraic Equations part 1 docx
... columns of the matrix inverse of A (Đ2.1 and Đ2.3).ã Calculation of the determinant of a square matrix A (Đ2.3).If M<N,orifM=Nbut the equations are degenerate, then there areeffectively fewer equations ... set of equationsto be solved can bewritten as the N ìN set of equations (ATÃ A) Ã x =(ATÃb)(2.0.4)where ATdenotes the transpose of the matrix A. Equations (2.0.4) are called thenormal equations ... related by M equations. Thecoefficients aijwith i =1,2, ,M and j =1,2, ,N are known numbers, asare the right-hand side quantities bi, i =1,2, ,M.Nonsingular versus Singular Sets of Equations If...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... J.H., and Reinsch, C. 1971,Linear Algebra,vol.IIofHandbook for Automatic Com-putation(New York: Springer-Verlag).Westlake, J.R. 1968,A Handbook of Numerical Matrix Inversion and Solution of ... writeout equations only for the case of four equations and four unknowns, and with three different right-hand side vectors that are known in advance. You can write bigger matrices and extend the equations ... 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 Course in Numerical Analysis, 2nd...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... (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 page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 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 RECIPES ... the set of nlinear equations A · x = b.a[1 n][1 n],c[1 n] ,and d[1 n]areinput as the output of the routineqrdcmp and are not modified.b[1 n]is input as theright-hand side vector, and is...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... 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 Course in Numerical Analysis, 2nd ... backsubstitution.Thecom-bination of Gaussian elimination and backsubstitution yields a solution to the set of equations. The advantage of Gaussian elimination and backsubstitutionover Gauss-Jordanelimination ... reduced, and the increasing numbers of predictable zeros reduce the count to one-third), and 12N2M times, respectively.Each backsubstitution of a right-hand side is12N2executions of a similar...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
... the loop of the above fragment and (e.g.) divide by powers of ten,to keep track of the scale separately, or (e.g.) accumulate the sum of logarithms of the absolute values of the factors and the ... 1968,A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley).2.3 LU Decomposition and Its ApplicationsSuppose we are able to write the matrix A as a product of ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
... l++;}}The routines bandec and banbks are based on the Handbook routines bandet1 and bansol1 in[1].CITED REFERENCES AND FURTHER READING:Keller, H.B. 1968, Numerical Methods for Two-Point ... 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 ... York:McGraw-Hill),Đ9.11.Horn, R.A., and Johnson, C.R. 1985,Matrix Analysis(Cambridge: Cambridge University Press).2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations...
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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 (C) 1988-1992 by Cambridge University ... if the a’s and c’s are scalars, but as matrix inversion if the a’s and c’s arethemselves submatrices. Imagine doing the inversionof a very large matrix, of orderN =2m, recursively by partitions ... matricesa11a12a21a22 and c11c12c21c22(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=...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
... 56Chapter 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 University ... n], and the vectorsb[1 n] and x[1 n]are input, as is the dimensionn.Also input isalud[1 n][1 n],theLU decomposition of aas returned by ludcmp ,and the vectorindx[1 n]also returned by ... 58Chapter 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 University...
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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 ... America).A ⋅ x = bSVD “solution” of A ⋅ x = c solutions of A ⋅ x = c′ solutions of A ⋅ x = dnullspace of ASVD solution of A ⋅ x = drange of Adc(b)(a)Axbc′Figure 2.6.1. ... combination of the set of equations thatwe are trying to solve. The resolution of the paradox is that we are throwing awayprecisely a combination of equations that is so corrupted by roundoff error...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
... theWoodburyformula and successiveapplications of the Sherman-Morrison formula is now clarified by noting that, ifU is thematrix formedby columnsoutoftheP vectors u1, ,uP,andVis the matrix formed by columnsout ... applications.)ã Each of the rst N locations of ija stores the index of the array sa that containsthe first off-diagonal element of the corresponding row of the matrix. (If there areno off-diagonal elements ... from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software....
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