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Miscellaneous typos fixed

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VictorianHues
2024-09-30 23:14:53 +02:00
parent 024429bceb
commit 82cfa1d44b
8 changed files with 32 additions and 32 deletions
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notebooks/LEQ.ipynb
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@@ -103,7 +103,7 @@
"### Problem statement\n",
"\n",
"Let us consider a system of linear equations written in matrix form $Ax=b$, where $A$ is a nonsingular square matrix, and $x$ and $b$ are vectors. $A$ and $b$ are given, and $x$ is unknown. The goal of Gaussian elimination is to transform the system $Ax=b$, into a new system $Ux=c$ such that\n",
"- both system have the same solution vector $x$,\n",
"- both systems have the same solution vector $x$,\n",
"- the matrix $U$ of the new system is *upper triangular* with unit diagonal, namely $U_{ii} = 1$ and $U_{ij} = 0$ for $i>j$.\n",
"\n",
"\n",
@@ -398,7 +398,7 @@
"source": [
"### Data partition\n",
"\n",
"Let start considering a row-wise block partition, as we did in previous algorithms.\n",
"Let's start considering a row-wise block partition, as we did in previous algorithms.\n",
"\n",
"In the figure below, we use different colors to illustrate which entries are assigned to a CPU. All entries with the same color are assigned to the same CPU."
]
@@ -454,7 +454,7 @@
"<b>Definition:</b> *Load imbalance*: is the problem when work is not equally distributed over all processes and consequently some processes do more work than others.\n",
"</div>\n",
"\n",
"Having processors waiting for others is a waist of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.\n"
"Having processors waiting for others is a waste of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.\n"
]
},
{