00000MA486052002
Pages: 2

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Max. Marks: 100

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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Eighth semester B.Tech degree examinations, September 2020

Course Code: MA486
Course Name: Course Name: ADVANCED NUMERICAL TECHNIQUES

PARTA
Answer any two full questions, each carries 15 marks

Find the largest eigen value and the corresponding eigen vector of the matrix by
2 -1 0

using power method. ட 2 3
0 -1 2

Solve the equations 102 + ‏ر2 ,13 = 2 + 101 + 2 ,12 = 2 + ہر‎ + 29 + 102 =
14 by Factorization method.

Find the orthogonal projection of (1,1,1) on (2,4,4). Also represent the first vector
as the sum of two orthogonal vectors.

Let V be the vector space of polynomials with inner product

= i f(t)g(dt. Using Gram-Schmidt process find an orthonormal
basis for V from the basis {1, t, (2).

Derive Cauchy-Schwarz inequality.

11 14

Find Singular Value Decomposition for the matrix ۶ 7 -2

PART छ
Answer any two full questions, each carries 15 marks
Evaluate A*[(1 — x)(1 - 2x)(1 — 3x)(1 —4x)], where A 15 the forward
difference operator. Assume the interval of difference being unity.

Find the lowest degree polynomial which takes the following values

೫ (0 ( 1 | 2 [3 [4 [5
४) | 0 [ 3 | 8 | 15 [ 24 | 35

Find the minimum of the function f(x) = (40 —90x)? using Golden section
method in the interval [0,1] with n = 6 (Three iterations).

Minimize f(A) = 0.65 — ‏ہت‎ — 0.654 ध्वा using Fibonacci method in the

interval [0,3], using n = 6.

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Duration: 3 Hours

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