Square root algorithms - Quiz
A) x0 >= S B) x0 = 0 C) x0 < 0 D) x0 > 0
A) S != 1 B) S > 0 C) S = 0 D) S < 0
A) x_n <= 0 B) x_n < 0 C) x_n > 0 D) x_n = 0
A) (x_n / sqrt(S)) - 1 B) S / x_n - 1 C) (sqrt(S) / x_n) - 1 D) x_n / S - 1
A) epsilon_n < -1 B) epsilon_n >= 0 C) epsilon_n <= 0 D) epsilon_n > -1
A) S * (1 + epsilon_n) B) sqrt(S) * (1 + epsilon_n) C) S / (1 + epsilon_n) D) sqrt(S) * epsilon_n
A) epsilon_n2 / (2(1 + epsilon_n)) B) 2 * epsilon_n2 / (1 + epsilon_n) C) epsilon_n2 / (1 + epsilon_n) D) epsilon_n / (2(1 + epsilon_n))
A) epsilon_{n+1} <= -1 B) epsilon_{n+1} >= 0 C) epsilon_{n+1} = -1 D) epsilon_{n+1} < 0
A) min { epsilon_n2 / 2, epsilon_n / 2 } B) min { epsilon_{n+1}2, epsilon_{n+1} } C) min { epsilon_{n+1} / 2, epsilon_{n+1}2 / 4 } D) min { epsilon_{n+1}2 / 2, epsilon_{n+1} / 2 }
A) Quadratic B) Cubic C) Linear D) Logarithmic
A) The cube root B) The non-negative square root C) The negative square root D) The reciprocal
A) Rational B) Prime numbers C) Irrational D) Integers
A) To infinite precision B) To some finite precision C) By guessing the exact value D) Using exact fractions
A) A series of increasingly accurate approximations B) A geometric progression of errors C) A single exact formula D) A random sequence of numbers
A) They are iterative B) They are non-computable C) They are linear D) They are always exact
A) Squaring the number S B) Calculating the final error C) Dividing by zero D) Choosing a suitable initial estimate
A) A Taylor series is integrated B) The algorithm terminates immediately C) The number S is discarded D) An iterative refinement is performed
A) Until some termination criterion is met B) When the estimate becomes zero C) When the computer crashes D) After exactly two steps
A) Euclid's method B) Taylor's method C) Newton's method D) Babylonian division
A) If division is much more costly than multiplication B) If infinite precision is required C) If division is faster than multiplication D) If S is a negative number
A) Using geometric proofs B) Using logarithmic addition C) Using Taylor series D) Using prime factorization
A) Decimal expansions B) Continued fraction expansions C) Fourier series expansions D) Binomial expansions
A) The programming language syntax exclusively B) The user's age and location C) Only the color of the output screen D) Needed accuracy, available tools, and computational power
A) Ancient, medieval, and futuristic B) Fast, slow, and impossible C) Mental calculation, paper and pencil, and digital computers D) Integer, fraction, and decimal
A) The size of the input number S B) How many iterations are required to achieve a specified precision C) The speed of the computer processor D) The total memory used by the program
A) Termination criterion B) Computational complexity C) Error propagation D) Initial estimation
A) All iterative methods B) Paper-and-pencil synthetic division and series expansion C) Babylonian approximation methods D) Heron's method and Newton's method
A) A square root calculated without decimals B) The square root rounded or truncated to the nearest integer C) The square root multiplied by an integer D) The exact square root of a prime number
A) Since the 20th century CE B) Since the Renaissance in Western Europe C) Since the invention of digital computers D) Since at least the period of ancient Babylon in the 17th century BCE
A) Three B) Ten C) One D) Five
A) A prime number B) A cube's volume C) A circle's area D) A hypotenuse
A) The first ascertainable algorithm for computing square root B) The first digital computer program C) The last manual square root method D) An exact formula for irrational numbers
A) During the construction of the Egyptian pyramids B) After introduction of the Arabic numeral system to western Europe C) In the 21st century D) During the ancient Babylonian period
A) Western Europe in the early Renaissance B) Ancient Mesopotamia C) South America in pre-Columbian times D) East Asia in the Middle Ages
A) As a language construct, compiler intrinsic, library function, or hardware operator B) Using paper and pencil simulation C) Exclusively via continued fractions D) Only through manual user input
A) Zero B) A negative number C) A non-zero positive number D) Any real number
A) More required iterations B) Faster convergence C) Higher memory usage D) Slower convergence
A) It does not converge at all B) It converges at the exact same speed C) It converges much slower D) It converges slightly faster
A) a < 10 B) a < 100 C) a <= 1 D) a < 1000
A) Into logarithmic scales only B) Into infinite continuous curves C) Into negative domains D) Into intervals
A) 3.16 B) 6.0 C) 4.0 D) 5.5
A) a = 1 B) a = 5.5 C) a = 100 D) a = 10
A) 100% B) 50% C) 4% D) 10%
A) Exponential curve B) Horizontal asymptote C) Vertical median D) Least-squares regression line
A) 50% B) 10% C) 30% D) 17%
A) Piece-wise linear approximation B) Constant rounding C) Logarithmic interpolation D) Cubic spline extrapolation
A) Use random sampling B) Use secant lines exclusively C) Use quadratic polynomials D) Use tangent lines
A) 372.8 B) 256 C) 354.0 D) 125348
A) 0.086 B) 19 C) 3.0 D) 5.3
A) 8 bits B) 2 bits C) 16 bits D) 4+ bits
A) The sign bit B) The high bit C) The exponent D) The low bit
A) 512 bytes B) 256 bytes C) 128 bytes D) 64 bytes
A) 11101101_2 B) 10101110_2 C) 0100_2 D) 11101001_2
A) 10101110_2 B) 11101101_2 C) 01101011_2 D) 11101001_2
A) A modern computer scientist B) A first-century Greek mathematician C) A twelfth-century Greek philosopher D) A sixth-century Babylonian king
A) Arithmetica B) Almagest C) Elements D) Metrica
A) AD 60 B) 60 BC C) AD 600 D) 160 AD
A) Yes, extensive clay tablets exist B) Yes, mentioned in Babylonian poetry C) No evidence exists D) Yes, recorded by Babylonian astronomers
A) Quadratically convergent B) Cubically convergent C) Logarithmically convergent D) Linearly convergent
A) Quaternions B) Complex numbers C) p-adic numbers D) Imaginary numbers
A) 1000 B) 400 C) 350 D) 600
A) 600.0 B) 354.0452 C) 357.1868 D) 404.456666666
A) 357.186837334 B) 404.456666666 C) 600.0 D) 354.0590
A) Seven B) Fifteen C) Ten D) Five
A) 28 B) 6 C) 23 D) 22
A) 23 B) 28 C) 6 D) 22
A) 23 B) 28 C) 6 D) 22
A) sqrt_Newton B) sqrt_Heron C) sqrt_approximate D) sqrt_p_adic
A) The true square root value B) The difference between successive estimates C) The convergence constant D) The absolute error
A) When C is greater than 1 B) When the successive differences become sufficiently small C) When delta_n equals the true value S D) When the absolute error is zero
A) Linear B) Quartically C) Quadratic D) Cubic
A) Roughly doubles B) Triples C) Roughly quadruples D) Increases by one
A) -199.5433 B) -195.5433 C) -190.5433 D) -195.4533
A) -195 B) -200 C) -205 D) -196
A) 450 B) 600 C) 400 D) 350
A) 400 B) 350 C) 600 D) 354
A) 355.06857 B) 350.06857 C) 354.06857 D) 354.60857
A) 354.045194 B) 354.450194 C) 350.045194 D) 354.06857
A) 10 digits B) 6 digits C) 4 digits D) 8 digits
A) Isaac Newton B) Babylonians C) Napier D) François Viète
A) No, only base 16 B) Yes C) No, only base 10 D) No, only base 2
A) A Pascaline B) An abacus C) A slide rule D) Napier's bones
A) Nothing B) 00 C) 11 D) The decimal point
A) 20px <= c B) x(20p + x) <= c C) x(10p + x) <= c D) x(p + x) <= c
A) p squared B) 20p + x C) x(20p + x) D) c - x
A) Old p plus x B) Old p times 20 plus x C) x times 10 plus p D) Old p times 10 plus x
A) Subtract y from c B) Multiply c by y C) Add y to c D) Divide c by y
A) 12.34 B) 11.45 C) 15.22 D) 13.24
A) It cannot be implemented on fixed-point hardware B) It converges very slowly compared to other methods C) Numerical errors accumulate D) It requires more storage space than lookup tables
A) 1960 B) 1975 C) 1950 D) 1940
A) UNIVAC I B) EDSAC C) ENIAC D) Manchester Baby
A) Robert Elliot Goldschmidt B) Isaac Newton C) Edmond Halley D) Babylonian scholars
A) 41 divided by 29 B) 99 divided by 70 C) 17 divided by 12 D) 5 divided by 2
A) Quadratic irrationals B) Denominators C) Remainders D) Convergents
A) 11 B) 00 C) 01 D) 10
A) The base-10 logarithm B) The base-2 logarithm C) The exponential function D) The natural logarithm
A) 0x3FC00000 B) 0x3F800000 C) 0x4B0D2000 D) 0x00000001
A) 524288 B) 1056964608 C) 2130706432 D) 1065353216
A) 0x1FBB4F2E B) 0x3F800000 C) 0x3FC00000 D) 0xFC00000
A) The number of bits in the mantissa B) The base of the logarithm C) The error adjustment constant D) The exponent bias |
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