the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where...

theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares, such that...

Least squares For the "sum of squared differences", see Mean squared error For the "sum of squared error", see Residual sum of squares For the "sum of squares...

method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the...

Least trimmed squares (LTS), or least trimmed sum of squares, is a robust statistical method that fits a function to a set of data whilst not being unduly...

Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of four squares (of integers)...

a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals...

represented as a sum of four non-negative integer squares. That is, the squares form an additive basis of order four: p = a 2 + b 2 + c 2 + d 2 , {\displaystyle...

A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables...

squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a...

least squares function approximation applies the principle of least squares to function approximation, by means of a weighted sum of other functions. The...

Exponentiation by squaring Hilbert's seventeenth problem, for the representation of positive polynomials as a sum of squares of rational functions Metric tensor...

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems...

minimising a sum of squares function S = ∑ i = 1 n ε i 2 = ∑ i = 1 n ( Y i − β 0 − β 1 ϕ 1 ( X i 1 ) − ⋯ − β p ϕ p ( X i p ) ) 2 . {\displaystyle S=\sum _{i=1}^{n}\varepsilon...

a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is...

of the squares of the errors—that is, the average squared difference between the estimated values and the true value. MSE is a risk function, corresponding...

needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences...

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters...

squares function r 2 ( n ) {\displaystyle r_{2}(n)} is defined as the number of ways of writing the number n {\displaystyle n} as the sum of two squares. Then...

Square-summable may refer to: Square-integrable functions Square-summable sequences; see Hilbert space § Sequence spaces This disambiguation page lists...

)}/2} SUM(x2): The sum of squares of the values is important in order to calculate the Standard Deviation of groups SUM ⁡ ( X 2 ⊎ Y 2 ) = SUM ⁡ ( X 2...

theory of theta functions. In the context of Waring's problem, powers of theta functions are the generating functions for the sum of squares function. Their...

perfect squares. Three squares are not sufficient for numbers of the form 4k(8m + 7). A positive integer can be represented as a sum of two squares precisely...

expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as...

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...

least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the...

excludes squares. The operator ( − 1 ) F {\displaystyle (-1)^{F}} that distinguishes fermions and bosons is then none other than the Möbius function μ ( n...

G(a_{n};x)=\sum _{n=0}^{\infty }a_{n}x^{n}.} If an is the probability mass function of a discrete random variable, then its ordinary generating function is called...

{\displaystyle \pi (x)=\sum _{p\leq x}1} A related function counts prime powers with weight 1 for primes, 1/2 for their squares, 1/3 for cubes, etc. It...

{sinc} (3)+\operatorname {sinc} (4)+\cdots ={\frac {\pi -1}{2}}.} The sum of the squares also equals ⁠π − 1/2⁠: ∑ n = 1 ∞ sinc 2 ⁡ ( n ) = sinc 2 ⁡ ( 1 ) +...