CSIR NET Part C
Counterexample bank
Part C is won by knowing which tempting claims are false. 149 counterexamples; 86 free to read right now. Pick your subject below.
Knowing the claim is false is half of it. The mistakes that cost marks shows the wrong options candidates actually pick, and the reasoning slip behind each one.
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Tagged “numerical”
“Newton's method converges quadratically to any root”
False — at the root 0
“Newton's method always converges from any starting point”
“Increasing the number of equally spaced interpolation nodes improves the approximation”
False — Runge's function on [−1, 1]
“A convergent method is stable for any step size”