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Page "Gaussian elimination" ¶ 35
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At and end
At the pool's far end was the little cabana Joyce had mentioned, and on the water's surface floated scattered lavender patches of limp-looking lather.
At either end and in the center there are bays which contain nine greater alcoves as frescoed and capacious as church apses.
At the beginning of the play she has partial illumination and at the end she has complete illumination, but there has been no question but that she moves toward the dark.
At four-o'clock, or four-thirty, the coming of the newsboy marked the end of the day ; ;
At the end of this period two pious Christians in Rome receive the revelation which leads them to seek the next Pope on the rock.
At the end of World War 2,, free Europe was ready for a new beginning.
At the very end, when the audience was silent and breathless, a collection was taken and then slowly everyone filed out.
At the end of the monologue the audience would applaud.
At the end of a shaft of light, the pews appeared to be broad stairs in a long dungeon.
At the end of the room there was a desk heaped with papers, and she began to riffle these, making sighs and and noises of girlish exasperation.
At the other end of the spectrum, where the more advanced countries can be relied upon to make well thought through decisions as to project priorities within a consistent program, we should be prepared to depart substantially from detailed project approval as the basis for granting assistance and to move toward long-term support, in cooperation with other developed countries, of the essential foreign exchange requirements of the country's development program.
At the end of its letter was the information that applicants for this position `` must also be prepared to teach costume design and advertising art ''.
At the end of the run, the strips in the third and sixth positions in each chamber were dried, stained for 1 hr, washed and dried, while the other strips were maintained in a horizontal position at 1-degree-C.
At the end of work one day, the personnel man took the applicants one at a time, asked them to sit behind the receptionist's desk and he then played the role of a number of people who might come to the receptionist with a number of queries and for a number of purposes.
At the end of this pass, the table indicates which index words and electronic switches are not available for assignment to symbolic references.
At the same time, every device that can be employed to reduce the number of variables is of the greatest value, and it is one of the attractive features of dynamic programming that room is left for ingenuity in using the special features of the problem to this end.
At the end of the calculated time he'd nose the Waco down through the cloud bank and hope to break through where some feature of the winter landscape would be recognizable.
At the end of the performance, Dave and Max came out into the brilliantly lit foyer among a surge of gowned and tuxedoed first nighters.
At the end of the half-hour, racking his brains, thinking over and over again of Kitti, her friends, her past, he left the bedroom.
At the end of the corridor Alec noticed a door marked: Fire Stairs.
At the end of the program, indeed, there was a demonstration that lasted for forty-five minutes, and nothing could stop it.
At war's end leadership in Western Europe passed from Britain because the Labour Government devoted its attention to the creation of a welfare state.
At the end of the Devonian period (), the seas, rivers and lakes were teeming with life but the land was the realm of early plants and devoid of vertebrates though some, such as Ichthyostega, may have sometimes hauled themselves out of the water.
At the American publisher's insistence, Burgess allowed their editors to cut the redeeming final chapter from the U. S. version, so that the tale would end on a darker note, with Alex succumbing to his violent, reckless nature — an ending which the publisher insisted would be ' more realistic ' and appealing to a U. S. audience.
At the end of World War II the US Army occupied Obersalzberg, to prevent Hitler from retreating with the Wehrmacht into the mountains.

At and algorithm
At this stage in the algorithm, it is required that terms with zero-valued coefficients are dropped, so that only binary coefficients equal to one are counted, thus the problem of multiplication or division by zero is not an issue, despite this implication in the factored equation:
At each step of the algorithm, some output is derived from x < sub > n + 1 </ sub >; the output is commonly either the bit parity of x < sub > n + 1 </ sub > or one or more of the least significant bits of x < sub > n + 1 </ sub >.
At the termination of the algorithm, the forest has only one component and forms a minimum spanning tree of the graph.
At each step of the algorithm, the node with the lowest value is removed from the queue, the and values of its neighbors are updated accordingly, and these neighbors are added to the queue.
At Rothamsted he worked on the design of experiments, including contributions to the theory of analysis of variance and originating Yates's algorithm and the balanced incomplete block design.
At each node c, the algorithm checks whether c can be completed to a valid solution.
At the end of the algorithm there are no edges left, and the sequence in which the edges was chosen forms an Eulerian cycle if the graph has no vertices of odd degree, or an Eulerian trail if there are exactly two vertices of odd degree.
At the end of 1999, MP3. com launched a promotion called " Pay for Play ," or P4P, involving an algorithm to pay each MP3. com artist on the basis of the number of streams and downloads of their songs.
At each step, the algorithm chooses the variable whose value to set, as follows:
Each iteration of the algorithm calculates a discrepancy d. At iteration k this would be:
At each iteration of the algorithm, each ant moves from a state to state, corresponding to a more complete intermediate solution.
At the start and end of the algorithm, extra key material is XORed with the block ( key whitening ).
At the age of 17, he co-authored a research manuscript (" A New Algorithm for Fixed-point Quantum Search ") with Lov Grover, the inventor of a quantum search algorithm that goes by his name.
At each level, the algorithm needs to decide in which subtree to insert the new data object.
At CADCentre, the two Newells and Tom Sancha developed Newell's algorithm, a technique for eliminating cyclic dependencies when ordering polygons to be drawn by a computer graphics system.
At time the current plant state is sampled and a cost minimizing control strategy is computed ( via a numerical minimization algorithm ) for a relatively short time horizon in the future:.
At the center is shown the new vertex, a shortest path tree as computed by the Bellman Ford algorithm with as starting vertex, and the values computed at each other node as the length of the shortest path from to that node.
At the line search step ( 4 ) the algorithm might either exactly minimize h, by solving, or loosely, by asking for a sufficient decrease in h. One example of the former is conjugate gradient method.
At each iteration of the algorithm, Mehrotra's predictor corrector method uses the same Cholesky decomposition to find two different directions: a predictor and a corrector.
At a first glance, one might think that the second variant of the algorithm is slower than the first, since it changes the value of some of the entries twice.
At which point the normal Bellman-Ford algorithm is used to recover a new route.
At first, security of the system was regained, with software revisions, manipulation of the Nagravision encryption algorithm, along with the phasing out of older cards, like the ROM101, ROM102, ROM103 in USA and ROM110, ROM120, ROM130 in Europe, in favour of the newer ROM142 / ROM180 / ROM182.
At the April 2012 NAB show Brevity introduced a customized algorithm for the accelerated transport and encoding of DNxHD files
At each step, the algorithm finds the largest element with a nonzero direction, and swaps it in the indicated direction:

1.248 seconds.