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Matrices provide a convenient mechanism to manage large amounts of data. Ordinary matrix multiplication is O(n3). With very large matrices, even shaving a small amount off the cost can still give you a worthwhile cost savings. The following reference is an example of using matrix multiplication. Implement Strassen's Algorithms in CLRS Chapter 4.2 using Python Or Java. It is only necessary to handle matrices where the size is a power of two. Implement ordinary multiplication and compare your results. Count individual multiplications to use as a basis for comparison. If you want to try timing, please do it in addition to, not instead of counting comparisons. A file with required input is provided. All input you create should be formatted the same: the first line should contain the order of the matrix, then the first matrix, in row major order, then the second matrix. This is followed by a blank line, then the order of the next matrix pair and so on. You need to collect enough data to have a meaningful comparison of the theoretical efficiency to the observed efficiency. Describe the time and space complexity as well. What is the theoretical efficiency compared to observed efficiency? Also include a table and graph showing observations with respect to asymptotic efficiency. Required Input 21 67 15 43 3 214 -1 2-1 0 -1201 3-10 2 2 3-1-2 -4 0-3 1 5 1 1 0 0 -2 12 10120-1-1-1 Calculate the square of this one. -1 1-1 1 2003 1-1 2-3-1 110 0232 10-1-2 2 3-1 0-1 0-1 0 12210112 3-10 22 221 2-2 1-3 3 012

Matrices provide a convenient mechanism to manage large amounts of data. Ordinary matrix multiplication is O(n3). With very large matrices, even shaving a small amount off the cost can still give you a worthwhile cost savings. The following reference is an example of using matrix multiplication. Implement Strassen's Algorithms in CLRS Chapter 4.2 using Python Or Java. It is only necessary to handle matrices where the size is a power of two. Implement ordinary multiplication and compare your results. Count individual multiplications to use as a basis for comparison. If you want to try timing, please do it in addition to, not instead of counting comparisons. A file with required input is provided. All input you create should be formatted the same: the first line should contain the order of the matrix, then the first matrix, in row major order, then the second matrix. This is followed by a blank line, then the order of the next matrix pair and so on. You need to collect enough data to have a meaningful comparison of the theoretical efficiency to the observed efficiency. Describe the time and space complexity as well. What is the theoretical efficiency compared to observed efficiency? Also include a table and graph showing observations with respect to asymptotic efficiency. Required Input 21 67 15 43 3 214 -1 2-1 0 -1201 3-10 2 2 3-1-2 -4 0-3 1 5 1 1 0 0 -2 12 10120-1-1-1 Calculate the square of this one. -1 1-1 1 2003 1-1 2-3-1 110 0232 10-1-2 2 3-1 0-1 0-1 0 12210112 3-10 22 221 2-2 1-3 3 012

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Matrices provide a convenient mechanism to manage large amounts of data. Ordinary matrix multiplication is O(n3). With very large matrices, even shaving a small amount off the cost can still give you a worthwhile cost savings. The following reference is an example of using matrix multiplication. Implement Strassen's Algorithms in CLRS Chapter 4.2 using Python Or Java. It is only necessary to handle matrices where the size is a power of two. Implement ordinary multiplication and compare your results. Count individual multiplications to use as a basis for comparison. If you want to try timing, please do it in addition to, not instead of counting comparisons. A file with required input is provided. All input you create should be formatted the same: the first line should contain the order of the matrix, then the first matrix, in row major order, then the second matrix. This is followed by a blank line, then the order of the next matrix pair and so on. You need to collect enough data to have a meaningful comparison of the theoretical efficiency to the observed efficiency. Describe the time and space complexity as well. What is the theoretical efficiency compared to observed efficiency? Also include a table and graph showing observations with respect to asymptotic efficiency. Required Input 21 67 15 43 3 2 1 4 -1 2-1 0 -1 201 3-10 2 2 3-1-2 -4 0-3 1 5 1 1 0 0 -2 12 C 10120-1-1-1 Calculate the square of this one. -1 1-1 1 2 003 1-1 2-3-1 1 10 0 2 32 10-1-2 2 3-1 0-1 0-1 0 122101 12 3-10 2 2 2 2 1 2-2 1-3 3 012
Transcribed Image Text:Matrices provide a convenient mechanism to manage large amounts of data. Ordinary matrix multiplication is O(n3). With very large matrices, even shaving a small amount off the cost can still give you a worthwhile cost savings. The following reference is an example of using matrix multiplication. Implement Strassen's Algorithms in CLRS Chapter 4.2 using Python Or Java. It is only necessary to handle matrices where the size is a power of two. Implement ordinary multiplication and compare your results. Count individual multiplications to use as a basis for comparison. If you want to try timing, please do it in addition to, not instead of counting comparisons. A file with required input is provided. All input you create should be formatted the same: the first line should contain the order of the matrix, then the first matrix, in row major order, then the second matrix. This is followed by a blank line, then the order of the next matrix pair and so on. You need to collect enough data to have a meaningful comparison of the theoretical efficiency to the observed efficiency. Describe the time and space complexity as well. What is the theoretical efficiency compared to observed efficiency? Also include a table and graph showing observations with respect to asymptotic efficiency. Required Input 21 67 15 43 3 2 1 4 -1 2-1 0 -1 201 3-10 2 2 3-1-2 -4 0-3 1 5 1 1 0 0 -2 12 C 10120-1-1-1 Calculate the square of this one. -1 1-1 1 2 003 1-1 2-3-1 1 10 0 2 32 10-1-2 2 3-1 0-1 0-1 0 122101 12 3-10 2 2 2 2 1 2-2 1-3 3 012
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