It is proved that the obtained exponential integrator can exactly preserve the quadratic energy. In comparison with the functionally-fitted energy-preserving methods whose numerical performance depends on the fitted frequency, the new exponential integrators are independent of the fitted frequency and ...
linear and exponential functions. Include comparisons of two functions presented algebraically.) MCC9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.★★★ MCC9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior...
($numbers); $quadratic_mean = Average::quadraticMean($numbers); // same as rootMeanSquare $root_mean_square = Average::rootMeanSquare($numbers); // same as quadraticMean $trimean = Average::trimean($numbers); $interquartile_mean = Average::interquartileMean($numbers); // same as iqm...
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This suggests that for cryptographic applications EC-LCG should be used with great care. For thelinear congruential generatorsimilar problems have been introduced by Knuth [26] and then considered in [7,13,23,27]; see also the surveys [8,28]. Thequadratic congruential generatorand theinverse co...
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A nonlinear function can look like the following examples; \(f(x) = x^2\) which is a quadratic function, \(f(x) = 2^x\) which is an exponential function, and \(f(x) = x^3 – 3x\) which is a cubic function. Example of a nonlinear function: \(f(x) = 200 – x^2\) ...
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with problem size. Furthermore, QLSAs cannot use an approximate ...
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