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Ensemble Square Root Filters
, 2003
"... Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics ..."
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Cited by 116 (7 self)
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of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.
The Square Root of NOT
, 1995
"... Digital computers are built out of circuits that have definite, discrete states: on or off, zero or one, high voltage or low voltage. Engineers go to great lengths to make sure these circuits never settle into some intermediate condition. Quantummechanical systems, as it happens, offer a guarantee ..."
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Digital computers are built out of circuits that have definite, discrete states: on or off, zero or one, high voltage or low voltage. Engineers go to great lengths to make sure these circuits never settle into some intermediate condition. Quantummechanical systems, as it happens, offer a guarantee of discreteness without any engineering effort at all. When you measure the spin orientation of an electron, for example, it is always either "up " or "down, " never in between. Likewise an atom gains or loses energy by making a "quantum jump" between specific energy states, without passing through intermediate energy levels. So why not build a digital computer out of quantummechanical devices, letting particle spins or the energy levels of atoms stand for binary units of information? One answer to this "Why not? " question is that you can't avoid building a quantummechanical computer even if you try. Since quantum mechanics appears to be a true theory of nature, it governs all physical systems, including the transistors and other components of the computer on your desk. All the same, quantum effects are seldom evident in electronic devices; components and circuits are designed so that the quantum states of many millions of electrons are averaged together, blurring their discreteness. In a quantum computer, the basic working parts would probably have to be individual electrons or atoms, and so another answer to the "Why not?" question is that building such a machine is simply beyond our skills. And
Fixed Point Square Root
, 1994
"... Abstract: The square root of a fixedpoint number is computed using a simple method similar to longhand division. ..."
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Abstract: The square root of a fixedpoint number is computed using a simple method similar to longhand division.
On Hadamard Square Roots of Unity
, 1999
"... A series all of whose coefficients have unit modulus is called an Hadamard square root of unity. We investigate and partially characterise the algebraic Hadamard square roots of unity. ..."
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A series all of whose coefficients have unit modulus is called an Hadamard square root of unity. We investigate and partially characterise the algebraic Hadamard square roots of unity.
Squares and Square Roots
"... ABSTRACT: In this article I am giving easy and simple methods / (KHAS methodKamal Haldar’s Addition and Subtraction method) to solve squares and square roots. After knowing these methods learner can solve the problems in a short way without using the number of steps, It is said that ..."
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ABSTRACT: In this article I am giving easy and simple methods / (KHAS methodKamal Haldar’s Addition and Subtraction method) to solve squares and square roots. After knowing these methods learner can solve the problems in a short way without using the number of steps, It is said that
Computing the Inverse Square Root
, 1994
"... Abstract: The inverse square root of a number is computed by determining an approximate value by table lookup and refining it through iteration. ..."
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Abstract: The inverse square root of a number is computed by determining an approximate value by table lookup and refining it through iteration.
Algorithms for Square Roots of Graphs
 SIAM Journal on Discrete Mathematics
, 1991
"... The nth power (n 1) of a graph G = (V; E), written G n , is defined to be the graph having V as its vertex set with two vertices u; v adjacent in G n if and only if there exists a path of length at most n between them. Similarly, graph H has an nth root G if G n = H . For the case of n = 2, ..."
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Cited by 40 (0 self)
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, we say that G 2 is the square of G and G is the square root of G 2 . Here we give a linear time algorithm for finding the tree square roots of a given graph and a linear time algorithm for finding the square roots of planar graphs. We also give a polynomial time algorithm for finding the square
On square roots of Mmatrices
, 1982
"... The question of the existence and uniqueness of an Mmatrix which is a square root of an Mmatrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an Mmatrix. 1. ..."
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Cited by 11 (0 self)
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The question of the existence and uniqueness of an Mmatrix which is a square root of an Mmatrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an Mmatrix. 1.
Square root propagation
"... We propose a message propagation scheme for numerically stable inference in Gaussian graphical models which can otherwise be susceptible to errors caused by finite numerical precision. We adapt square root algorithms, popular in Kalman filtering, to graphs with arbitrary topologies. The method consi ..."
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Cited by 3 (0 self)
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We propose a message propagation scheme for numerically stable inference in Gaussian graphical models which can otherwise be susceptible to errors caused by finite numerical precision. We adapt square root algorithms, popular in Kalman filtering, to graphs with arbitrary topologies. The method
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