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This is a right inverse, as + =. In the more general case, the pseudoinverse can be expressed leveraging the singular value decomposition . Any matrix can be decomposed as A = U D V ∗ {\displaystyle A=UDV^{*}} for some isometries U , V {\displaystyle U,V} and diagonal nonnegative real matrix D {\displaystyle D} .
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...
The binary logarithm is the logarithm to the base 2 and is the inverse function of ... Binary logarithms ... type conversion such as MATLAB the argument to the log2 ...
Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.. Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in ...
Binary entropy is a special case of (), the entropy function. H ( p ) {\displaystyle \operatorname {H} (p)} is distinguished from the entropy function H ( X ) {\displaystyle \mathrm {H} (X)} in that the former takes a single real number as a parameter whereas the latter takes a distribution or random variable as a parameter.
Permutations that generalize the bit-reversal permutation by reversing contiguous blocks of bits within the binary representations of their indices can be used to interleave two equal-length sequences of data in-place. [4] There are two extensions of the bit-reversal permutation to sequences of arbitrary length.
The field requirement means that the Berlekamp–Massey algorithm requires all non-zero elements to have a multiplicative inverse. [1] Reeds and Sloane offer an extension to handle a ring. [2] Elwyn Berlekamp invented an algorithm for decoding Bose–Chaudhuri–Hocquenghem (BCH) codes.
A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I]