Numerical methods (Answers to the SYNERGY / MIT / MY te

Ready answers to the Numerical methods test.
Educational institution: SYNERGY, MY, MIT.
Delivery: fresh.
The result of passing is 95-100 points.
Below you can find questions on the Numerical Methods test.

QUESTIONS FOR THE TEST:
The sweep method consists of (answer) steps

(answer) the method is used if a fairly limited number of calculations are required to obtain the result and if the range within which the solution is valid is known

...dx is the ratio of the absolute error Dx to the absolute value of the approximate value x¢

In the Gauss method, reducing a system of linear equations to triangular form is (answer)

The method (answer) is based on the use of Taylor series expansion of functions, with terms containing second and higher order derivatives being discarded

In many cases, when a function is specified analytically, a certain interval is calculated using the formula (answer)

According to the theorem (answer), if the function f(x) is continuous on the interval [a, b], then for any e > 0 there is a polynomial j(x) of degree m = m(e), the absolute deviation of which from the function f(x) on the interval [a, b] is less than e

Computational methods are divided into direct and (answer)

For the system of linear algebraic equations (SLAE) given below, the free terms of the system are (answer)

For the system of linear algebraic equations (SLAE) given below, a₁₁a₁₂ (answer) aₙₙ is (answer)

To solve systems of linear equations with a tridiagonal matrix, the method is used (answer)

If we express the relative error (x) in terms of the absolute error x and the module of the approximate value x, we obtain: (answer)

If the coefficients ai of the function j(x) are determined from the equality condition f(xi) = j(xi), i.e. functions coincide at given known points, then this method of approximation is called (answer)

If one function is constructed over the entire interval, this is (answer) interpolation

The task (answer) of a function is to construct for a given function another function different from it, the values of which are sufficiently close to the values of this function

Using graphical methods for solving problems in mathematics, (answer)

An iterative numerical method for approximately finding the root of an equation is the method (answer)

The group of direct methods includes (answer)

The method (answer) is a method for solving systems of linear algebraic equations with the number of equations equal to the number of unknowns with a non-zero main determinant of the coefficient matrix of the system

Method (answer) also known as tangent method

The method (answer) is the simplest numerical method for solving the order of accuracy of (systems of) ordinary differential equations and has the first order of accuracy

Bisection method is another name for the method (answer)

The Gauss method and the Cramer method for systems of linear algebraic equations are related to (answer) methods for solving problems in mathematics

The solution obtained (answer) by the problem solving method may contain some error (error).

The essence of finite difference methods is that the region of continuous variation of the argument and function is replaced by a discrete set of points called (answer), which make up the difference grid

The condition for the existence of a root of a continuous function on an interval is (answer), which means that on a given interval the function changes sign, i.e. intersects the x axis

Root refinement is the calculation of an approximate value of the root with a given accuracy (answer)

Numerical integration formulas are called (answer)

You can find the roots of an algebraic equation with a certain accuracy using (answer) methods

It is not true that iterative methods include the method (answer)

It is not true that methods for solving a nonlinear equation include the method (answer)

It is not true that the methods of numerical integ