Explain why does Crout’s factorization can solve very large scale linear system easily and Gaussian elimination does not?

Answers

Answer 1

Crout's factorization is an indirect method of solving linear systems of equations that involves solving upper and lower triangular systems, as opposed to Gaussian elimination, which is a direct method.

Because Crout's factorization only needs to solve lower and upper triangular systems, it can solve very large-scale linear systems easily. Gaussian elimination is a direct approach that involves numerous elimination operations that must be performed on all the rows of the matrix to be inverted. The time taken for the Gaussian elimination algorithm to solve linear systems of equations is directly proportional to the order of the matrix, which means that the more complicated the system, the more time it will take to solve.

On the other hand, Crout's method factorization algorithm factorizes the system matrix into two triangular matrices that are then solved to find the solutions to the linear system of equations. Because it only needs to solve triangular systems, the Crout factorization algorithm is faster and more effective at solving very large linear systems of equations than Gaussian elimination.

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Related Questions

It is generally accepted that the word "kawanatanga" was not a good translation into te reo Maori of the term "sovereignty". The word that would have conveyed the idea more accurately would have been "mana" but that was not used most likely because:

a.Kawanatanga was already known to Maori through translation of the Bible into te reo.

b.The Williamses who provided the translation were sufficiently fluent in te reo to know that no rangatiratanga would agree to cede his or her mana.

c.The Williamses, father and son, who provided the translation were not sufficiently fluent in te reo.

Answers

The word that would have conveyed the idea of sovereignty more accurately would have been "mana" but that was not used most likely because the Williamses who provided the translation were not sufficiently fluent in te reo.

Kawanatanga refers to a term used in the Treaty of Waitangi, which is usually translated as "governorship" or "sovereignty." It was the concept of the Crown having supreme power and jurisdiction over the British colonies and their Maori inhabitants. It should be noted that the treaty was created in two languages: English and Te Reo Māori. In the English version of the treaty, the term used was "sovereignty," whereas in the Māori version, the term used was "kawanatanga," which means governance. The word "sovereignty" was not an accurate translation of the word "kawanatanga."

Instead, the term that would have conveyed the idea of sovereignty more accurately would have been "mana." It is believed that the Williamses, father and son, who provided the translation were not sufficiently fluent in te reo, which is why they used "kawanatanga" instead of "mana." Mana is a concept of authority or power that exists in Māori culture. A person's mana is their authority, power, and influence. It is possible that the Williamses were not aware of the full extent of the term's meaning and usage, which is why they chose to use "kawanatanga" instead.

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Provide three instructional strategies for
assisting students, one for use in the beginning stage of reading
development, one for
the intermediate
stage, and one for the advanced st

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Three instructional strategies for assisting students at different stages of reading development are:

In the beginning stage of reading development, students benefit from phonics instruction. Phonics instruction focuses on teaching students the sounds that letters and letter combinations make and how to blend these sounds to read words. This strategy helps students develop foundational skills in decoding and word recognition, which are crucial for reading fluency.

In the intermediate stage, guided reading is an effective strategy. Guided reading involves small-group instruction where students read texts at their instructional level with teacher support. The teacher provides guidance, models reading strategies, and facilitates discussions to enhance comprehension. This strategy allows students to practice reading independently while receiving feedback and support to improve their reading skills.

For students in the advanced stage of reading, literature circles are beneficial. Literature circles are small, student-led discussion groups where students read and analyze literature together. Each student takes on a specific role and engages in meaningful discussions about the text. This strategy promotes critical thinking, deepens comprehension, and encourages students to make connections between the text and their own experiences, other texts, and the world around them.

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whose belief in civil disobedience did the beats emulate? a. henry david thoreau b. lawrence ferlinghetti c. amiri baraka

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The Beat Generation, a group of American writers who emerged in the 1950s, was inspired by the philosophy of civil disobedience.

They were inspired by the writings of Henry David Thoreau, who advocated civil disobedience in his famous essay "Resistance to Civil Government." Therefore, the belief in civil disobedience that the Beats emulated was that of Henry David Thoreau. The Beats were influenced by Thoreau's idea that people should disobey unjust laws as a form of protest. They believed that it was their duty to speak out against social injustice and that this could only be achieved by breaking the law.

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