Let " p " be an interior point of the disk, and let " n " be a number that is divisible by four and greater than or equal to eight.
42.
Hence, every point in the Cantor set is an accumulation point ( also called a cluster point or limit point ) of the Cantor set, but none is an interior point.
43.
Its corrector step uses the same Cholesky decomposition found during the predictor step in an effective way, and thus it is only marginally more expensive than a standard interior point algorithm.
44.
The disadvantage of indirect methods is that the boundary-value problem is often extremely difficult to solve ( particularly for problems that span large time intervals or problems with interior point constraints ).
45.
Viviani's theorem generalizes to equilateral polygons : The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point.
46.
Viviani's theorem generalizes to equilateral polygons : The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point.
47.
The converse also holds : If the sum of the distances from an interior point of a triangle to the sides is independent of the location of the point, the triangle is equilateral.
48.
The vertices of the pedal triangle of an interior point " P ", as shown in the top diagram, divide the sides of the original triangle in such a way as to satisfy
49.
These algorithms are known to have fundamentally different characteristics; for example, interior point methods follow a path through the interior of the feasible region while active set methods tend to stay at the boundaries.
50.
The method is based on the fact that at each iteration of an interior point algorithm it is necessary to compute the Cholesky decomposition ( factorization ) of a large matrix to find the search direction.
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