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CE101 LE2 CHAP3
17問 • 2年前
  • John Rotrix Tumaneng
    • 通報

    問題一覧

  • 1

    A solution to the equation (also called a root of the equation) is a numerical value of x that satisfies the equation

    Analytical Solution

  • 2

    Analytical Solution is also called?

    a root of the equation

  • 3

    The solution is the point where the function f(x) crosses or touches the x-axis. An equation might have no solution or can have one or several (possibly many) roots

    Graphical Solution

  • 4

    A _______ of an equation f(x) = 0 is a valze of x that satisfies the equation approximately. This means that when x is substituted in the equation, the value of f(x) is close to zero but not exactly ZERO

    Numerical Solution

  • 5

    The two methods of solving equations numerically

    Bracketing Methods and Open Methods

  • 6

    The endpoints of the interval are the upper bound and lower bound of the solution. Then, by using a numerical scheme, the size of the interval is successively reduced until the distance between the endpoints is less than the desired accuracy of the solution

    Bracketing Method

  • 7

    An initial estimate(one point) for the solution is assumed. The value of this initial guess for the solution should be close to the actual solution. Then, by using a numerical scheme, better ( more accurate) values for the solution are calculated

    Open Method

  • 8

    When solving an equation numerically, one has to select the desired ________ of the solution

    Accuracy

  • 9

    The four measures that can be considered for estimating errors

    True Error Tolerance in f(x) Tolerance in the solution Relative Error

  • 10

    The _________ is the difference between the true solution and a numerical solution

    True Error

  • 11

    Instead of considering the error in the solution, it is possible to consider the deviation of the numerical solution from zero. The __________ is defined as the absolute value of the difference between the true solution and numerical solution

    Tolerance in f(x)

  • 12

    A _________ is the maximum amount by which the true solution can deviate from an approximate numerical solution. A ________ is useful for estimating the error when bracketing methods are used for determining the numerical solution.

    Tolerance in the solution

  • 13

    The two relative error

    True Relative Error Estimated Relative Error

  • 14

    The __________ is a bracketing method for finding a numerical solution of an equation of the form f(x) = 0 when it is known that, within a given interval [a,b], f(x) is continuous and the ewuation has a solution

    Regula Falsi Method

  • 15

    Regula Falsi Method is also called

    false position and linear interpolation methods

  • 16

    __________ if a scheme for finding a numerical solution of an equation of the form f(x) =0 where f(x) is continuous and differentiable, and the equation is known to have a solution near a given point.

    Newton's Method

  • 17

    Newton's Method is also called

    Newton-Raphson Method

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    14問 • 1年前
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    問題一覧

  • 1

    A solution to the equation (also called a root of the equation) is a numerical value of x that satisfies the equation

    Analytical Solution

  • 2

    Analytical Solution is also called?

    a root of the equation

  • 3

    The solution is the point where the function f(x) crosses or touches the x-axis. An equation might have no solution or can have one or several (possibly many) roots

    Graphical Solution

  • 4

    A _______ of an equation f(x) = 0 is a valze of x that satisfies the equation approximately. This means that when x is substituted in the equation, the value of f(x) is close to zero but not exactly ZERO

    Numerical Solution

  • 5

    The two methods of solving equations numerically

    Bracketing Methods and Open Methods

  • 6

    The endpoints of the interval are the upper bound and lower bound of the solution. Then, by using a numerical scheme, the size of the interval is successively reduced until the distance between the endpoints is less than the desired accuracy of the solution

    Bracketing Method

  • 7

    An initial estimate(one point) for the solution is assumed. The value of this initial guess for the solution should be close to the actual solution. Then, by using a numerical scheme, better ( more accurate) values for the solution are calculated

    Open Method

  • 8

    When solving an equation numerically, one has to select the desired ________ of the solution

    Accuracy

  • 9

    The four measures that can be considered for estimating errors

    True Error Tolerance in f(x) Tolerance in the solution Relative Error

  • 10

    The _________ is the difference between the true solution and a numerical solution

    True Error

  • 11

    Instead of considering the error in the solution, it is possible to consider the deviation of the numerical solution from zero. The __________ is defined as the absolute value of the difference between the true solution and numerical solution

    Tolerance in f(x)

  • 12

    A _________ is the maximum amount by which the true solution can deviate from an approximate numerical solution. A ________ is useful for estimating the error when bracketing methods are used for determining the numerical solution.

    Tolerance in the solution

  • 13

    The two relative error

    True Relative Error Estimated Relative Error

  • 14

    The __________ is a bracketing method for finding a numerical solution of an equation of the form f(x) = 0 when it is known that, within a given interval [a,b], f(x) is continuous and the ewuation has a solution

    Regula Falsi Method

  • 15

    Regula Falsi Method is also called

    false position and linear interpolation methods

  • 16

    __________ if a scheme for finding a numerical solution of an equation of the form f(x) =0 where f(x) is continuous and differentiable, and the equation is known to have a solution near a given point.

    Newton's Method

  • 17

    Newton's Method is also called

    Newton-Raphson Method