The Lagrange’s formula can be used to obtain a ____________________

Bound on the error of interpolating polynomial

Numerical methods for solving linear algebraic system may be divided into two types, what are the types?

Direct and Iterative

If P(x) is a polynomial of degree \\(n>1\\) and \\(a_n\\neq 0\\), then P(x) has possible solutions as

Real or complex number

To understand the numerical methods for solving linear system of equations, it is necessary to have some knowledge of the properties of__________

Matrices

The method of determining an approximate value of f(x) for a non-tabular value of x which lies in the internal [a, b] is called?

Interpolation

If \\(f(x)=x^3\\) find the value of \\(f[a, b, c]\\)

\\(a+b+c\\)

Obtain the value of x when \\(y=3\\) from the values of \\(x=4, 7, 10, 12\\) corresponding to the values of \\(y=-1, 1, 2, 4\\)

23.1213

The values of \\(f(x)\\) at the given \\((n+1)\\) distinct point is called

Abscissas

In a finite difference, the error increases with the order of _____

Differences

If \\(f(x)=2x^3+3x^2-x+1\\), find \\(f[1,-1,2,3]\\)

2

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If \(\\mu\) is the mean operator, \ (\\mu^{2}=\)
Answer: \\(1 +\\frac{\\delta^{2}}{4}\\)

To find the solution vector \(x\) using the Gauss elimination method number of operations are required.
Answer: W(\\frac{nA{3}K6}+nA{2H\frac{nK4}\\)

Find the smallest positive root of \(2x\\ {\\mathrm{tan}x\\ }\\ =\\ 0\) by Newton- Raphson method, correct to 5 decimal places.
Answer: 1.165561

Evaluate the differences \(\\nablaA{3} [a_{3}xA{3}+a_{2}xA{2}+a_{1 }x\\ +\\ a_{0}]\).
Answer: \\(a_{3}3!hA{2}\\)

If \(P_{n}\\left(x\\right)\) is a polynomial of degree n with leadingcoefficient an, and \ (x_{0}\) is an arbitrary point, then \ (Wmath rm{\\Delta}A{n+1 }P_{n+1 }(x_{0})\\ =\)
Answer: \\(0\\)

Evaluate \(\\left|\\begin{array}{ccc}3 & 3 & 2\\\\2 & -3 & -1WW1 & 4 &1 \\end{array}\\right|\)
Answer: 16

The Taylor series expansion of is \(x-\\frac{xA{2}}{2}+\\frac{xA{3}K3}-\\frac{xA{4}K4}+\\dots\)J
Answer: \\(\\mathrm{ln}\\left(1 +x\\right)\\)

If \(\\mu\) is the mean operator and \(\\delta\) is the central difference then, \ (\\mu\\delta=\)
Answer: \\(\\frac{1}{2}\\left(\\mathrm{\\delta}\\mathrm{+}\\mathrm{\\na

The Taylor series expansion of is \(1 +x+xA{2}+xA{3}+\\dots\),
Answer: \\(\\frac{1 }{1 -x}\\)

Find an approximate value of \(\\sqrt[3]{26}\) using the mean value theorem.
Answer: 2.963

Find the eigenvalues of the matrix \ (\\left[\\begin{arrayXccc} 1 & 0 & OWW 0 & 2 & OUW 0 & 0 & 3 \\end{array}\\right]\)
Answer: \\(\\left(1,2,3\\right)\\)

If \(a=\\left(\\begin{arrayKccc}1 & 2 & 6\\\\2 & 4 & 1WW7 & 3 & 2 \\end{array}\\right)\), find \ (\\mathrm{det}\\left(A\\right)\\ \)
Answer: -13

If \(f(x)\\ =\\ xA{3}\), find the value of \(f[a,\\ b,W c]\)
Answer: a+b+c

The formula \(x_{n+1}=\\frac{x_{n- 1 }f\\left(x_{n}\\right)-x_{n}f\\left(x_{n- 1 }\\right)Kt\\left(x_{n}\\right)-t\\left(x_{n- 1}\\right)}\)is called method.
Answer: secant

Supposed that the product two matrices A and B is equal to an identity matrix, then matrix Bis of A
Answer: inverse

If \(a=AA{T}\)the \(a\) is called matrix
Answer: symmetric

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