1) a) Write a Matlab function program thomas(e.f.g.r.n) based on the pseudocode below which solves a tridiagonal system of n linear algebraic equations. Here e, f and g are vectors containing the tridiagonal elements of the coefficient matrix, r is the right hand side vector and x is the solution vector. €₂282 e3f 83 C-1 fn-1 B-1-1 e f. x₂ (a) Decomposition DOFOR K = 2, n ek = ex/fk-1. fk = fk - ek 9k-1 END DO (b) Forward substitution DOFOR K = 2, n rk = rk ek rk-l END DO (c) Back substitution Xn = rn /fn DOFOR k = n -1. 1, -1 Xx=(rk 9k Xx+1)/fk. END DO FIGURE 11.2 Pseudocode to implement the Thomas algorithm, an LU decomposition method for tridi- agonal systems, 7₂ 73 b) Write a Matlab main program which calls the function program developed in part (a) to solve the following tridiagonal system [X1 38-0 5 = 1 -2 3 -4 -6 c) Solve the tridiagonal system of equations in part (b) manually using the Thomas algorithm in part (a). Show the expression and the numerical value of each variable as it is computed. 2) After scaling the coefficient matrix given in problem (1b), calculate its (a) column-sum norm, (b) row-sum norm and (c) Euclidean (Frobeneus) norm.
1) a) Write a Matlab function program thomas(e.f.g.r.n) based on the pseudocode below which solves a tridiagonal system of n linear algebraic equations. Here e, f and g are vectors containing the tridiagonal elements of the coefficient matrix, r is the right hand side vector and x is the solution vector. €₂282 e3f 83 C-1 fn-1 B-1-1 e f. x₂ (a) Decomposition DOFOR K = 2, n ek = ex/fk-1. fk = fk - ek 9k-1 END DO (b) Forward substitution DOFOR K = 2, n rk = rk ek rk-l END DO (c) Back substitution Xn = rn /fn DOFOR k = n -1. 1, -1 Xx=(rk 9k Xx+1)/fk. END DO FIGURE 11.2 Pseudocode to implement the Thomas algorithm, an LU decomposition method for tridi- agonal systems, 7₂ 73 b) Write a Matlab main program which calls the function program developed in part (a) to solve the following tridiagonal system [X1 38-0 5 = 1 -2 3 -4 -6 c) Solve the tridiagonal system of equations in part (b) manually using the Thomas algorithm in part (a). Show the expression and the numerical value of each variable as it is computed. 2) After scaling the coefficient matrix given in problem (1b), calculate its (a) column-sum norm, (b) row-sum norm and (c) Euclidean (Frobeneus) norm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please answer part(s) 1- (C) and 2
Transcribed Image Text:1) a) Write a Matlab function program thomas(e.f.g.r.n) based on the pseudocode below which
solves a tridiagonal system of n linear algebraic equations. Here e, fand g are vectors
containing the tridiagonal elements of the coefficient matrix, r is the right hand side vector and
x is the solution vector.
₁82
ef 83
C-1 fa-1 B-1-1
er
f. J x₂
(a) Decomposition
DOFOR K = 2, n
ek =
ex/fk-1.
fk = fk - ek 9k-1
END DO
(b) Forward substitution
DOFOR K = 2, n
rk = rk ek rk-I
END DO
(c) Back substitution
Xn = rn /fn
DOFOR k = n -1. 1, -1
Xx=(rk 9k Xx+1)/fk
END DO
FIGURE 11.2
Pseudocode to implement the
Thomas algorithm, an LU
decomposition method for tridi-
agonal systems.
7₂
73
b) Write a Matlab main program which calls the function program developed in part (a) to solve
the following tridiagonal system
1
3
[x1
5 x₂ =
-2
-4
-6 7
c) Solve the tridiagonal system of equations in part (b) manually using the Thomas algorithm in
part (a). Show the expression and the numerical value of each variable as it is computed.
2) After scaling the coefficient matrix given in problem (1b), calculate its (a) column-sum norm, (b)
row-sum norm and (c) Euclidean (Frobeneus) norm.
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