In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle...

RMSD is the square root of the average of squared errors. The effect of each error on RMSD is proportional to the size of the squared error; thus larger...

Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science The square-root sum problem (SRS) is a computational...

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures...

squared deviations aka total sum of squares E ⁡ ( T − C ) = ( k − 1 ) σ 2 {\displaystyle \operatorname {E} (T-C)=(k-1)\sigma ^{2}} treatment squared deviations...

Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square...

The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written...

squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (1 × 1). Hence, a square with...

mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix...

the sum of the squared norms of orthogonal summands equals the squared norm of the sum. Least squares Mean squared error Squared deviations "Sum of Squares...

mathematics, a square root of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of...

digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits...

square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter i is ambiguous or problematic...

observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared is odd) modulo 4. Since the Diophantus identity implies...

square root of a number x is a number r which, when squared, becomes x: r 2 = x . {\displaystyle r^{2}=x.} Every positive real number has two square roots...

In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance...

two square roots. The square of the absolute value of a complex number is called its absolute square, squared modulus, or squared magnitude.[better source needed]...

}},} where the chi-squared is a weighted sum of squared deviations: χ 2 = ∑ i ( O i − C i ) 2 σ i 2 {\displaystyle \chi ^{2}=\sum _{i}{\frac {(O_{i}-C_{i})^{2}}{\sigma...

=n^{2}} with the sum being the square of the difference between the two (and thus the difference of the two being the square root of the sum): T n + T n −...

unity are not quadratic integers, but the sum of any root of unity with its complex conjugate (also an nth root of unity) is a quadratic integer. For n...

a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words, the sum of...

{\boldsymbol {\beta }}).} The least-squares method finds the optimal parameter values by minimizing the sum of squared residuals, S {\displaystyle S} : S...

integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of...

SSPE=nMSPE is called sum squared prediction error. The root mean squared prediction error is the square root of MSPE: RMSPE=√MSPE. The mean squared prediction error...

vector is determined by calculating its Euclidean norm: the square root of the sum of squares of the vector components. When each component of the vector...

worst-case error that grows proportional to n {\displaystyle n} , and a root mean square error that grows as n {\displaystyle {\sqrt {n}}} for random inputs...

establishing likelihood of obtaining the maximum and minimum values, such as Root Sum Square (RSS) or Monte-Carlo methods. In performing a tolerance analysis, there...

selected performance measure, in the sense that the least squares approach is related to the mean squared error, the equivalent for mean absolute error is least...

expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance...

In mathematics, a square-free polynomial is a univariate polynomial (over a field or an integral domain) that has no multiple root in an algebraically...