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The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xa and xb for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xb is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?
Initialize: xa, xb, ε, N // ε = convergence indicator
fb = f(xb) i = 0
while (i < N and |fb| > ε) do
i = i + 1 // update counter
xt = ? // missing expression for
// intermediate value
xa = xb // reset xa
xb = xt // reset xb
fb = f(xb) // function value at new xb
fb = f(xb) i = 0
while (i < N and |fb| > ε) do
i = i + 1 // update counter
xt = ? // missing expression for
// intermediate value
xa = xb // reset xa
xb = xt // reset xb
fb = f(xb) // function value at new xb
end while
if |fb| > ε
then // loop is terminated with i = N
write “Non-convergence”
else
write “return xb”
end if
if |fb| > ε
then // loop is terminated with i = N
write “Non-convergence”
else
write “return xb”
end if
- a)xb – (fb– f(xa)) fb/ (xb – xa)
- b)xa– (fa– f(xa)) fa/ (xb – xa)
- c)xb – (fb – xa) fb/ (xb – fb(xa)
- d)xa – (xb – xa) fa/ (fb – f(xa))
Correct answer is option 'D'. Can you explain this answer?
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The secant method is used to find the root of an equation f(x) = 0. It...
Understanding the Secant Method
The secant method is an iterative numerical technique used to approximate the roots of a function. It uses two starting points and applies linear interpolation to find a new estimate for the root.
Key Components of the Secant Method
- Initial Estimates: The process begins with two estimates, xa and xb.
- Function Evaluations: The values of the function at these points, f(xa) and f(xb), are essential for the iteration.
Missing Expression Explained
The missing expression in the iterative formula is crucial for updating the estimate of the root. The correct option is:
Option D: xa - (xb - xa) * fa / (fb - f(xa))
Why Option D is Correct
- Linear Interpolation: This expression is derived from the concept of linear interpolation based on the secant line connecting the points (xa, f(xa)) and (xb, f(xb)).
- Slope Calculation: The term (fb - f(xa)) represents the change in the function values, while (xb - xa) is the change in the x-values. This forms the basis for finding the next x-value.
- Update Rule: The expression effectively calculates a new estimate (xt) based on the previous estimates and function values, facilitating convergence towards the root.
Conclusion
In summary, the secant method's iterative process relies on calculating new estimates using linear interpolation. Option D accurately reflects this process, making it the suitable expression to fill in the missing part in the iteration.
The secant method is an iterative numerical technique used to approximate the roots of a function. It uses two starting points and applies linear interpolation to find a new estimate for the root.
Key Components of the Secant Method
- Initial Estimates: The process begins with two estimates, xa and xb.
- Function Evaluations: The values of the function at these points, f(xa) and f(xb), are essential for the iteration.
Missing Expression Explained
The missing expression in the iterative formula is crucial for updating the estimate of the root. The correct option is:
Option D: xa - (xb - xa) * fa / (fb - f(xa))
Why Option D is Correct
- Linear Interpolation: This expression is derived from the concept of linear interpolation based on the secant line connecting the points (xa, f(xa)) and (xb, f(xb)).
- Slope Calculation: The term (fb - f(xa)) represents the change in the function values, while (xb - xa) is the change in the x-values. This forms the basis for finding the next x-value.
- Update Rule: The expression effectively calculates a new estimate (xt) based on the previous estimates and function values, facilitating convergence towards the root.
Conclusion
In summary, the secant method's iterative process relies on calculating new estimates using linear interpolation. Option D accurately reflects this process, making it the suitable expression to fill in the missing part in the iteration.
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The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer?
Question Description
The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer?.
The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer?.
Solutions for The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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Here you can find the meaning of The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xaand xbfor the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xbis the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?Initialize: xa, xb, ε, N // ε = convergence indicatorfb = f(xb) i = 0while (i < N and |fb| > ε) doi = i + 1 // update counterxt = ? // missing expression for // intermediate valuexa = xb // reset xaxb = xt // reset xbfb = f(xb) // function value at new xbend whileif |fb| > εthen // loop is terminated with i = Nwrite “Non-convergence”elsewrite “return xb”end ifa)xb– (fb– f(xa)) fb/ (xb– xa)b)xa– (fa– f(xa)) fa/ (xb– xa)c)xb– (fb– xa) fb/ (xb– fb(xa)d)xa– (xb– xa) fa/ (fb– f(xa))Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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